Combinatorics

Problem 301

Monroe High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent.
Here are the positions and the people interested in each. \begin{tabular}{|c|l|} \hline Position & \multicolumn{1}{|c|}{ People interested } \\ \hline Faculty member & Mrs. Rodriguez, Ms. Scott, Dr. Miller \\ \hline Male student & Bob, Boris, Carlos, Justin, Dante, Shen \\ \hline Female student & Maya, Latoya, Laura, Rachel, Carmen, Martina \\ \hline Parent & Dr. Lopez, Mr. Green, Ms. Anderson, Ms. Martinez \\ \hline \end{tabular}
Based on this list, how many ways are there to fill the four committee positions? $\square$

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Problem 302

7. Given a portion of the periodic table below, write the complete equation for the alpha decay of Plutonium-242. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $\begin{array}{r} 89 \\ \text { Ac } \\ {[227.03]} \end{array}$ & $\begin{array}{c} 90 \\ \text { Th } \\ 232.04 \end{array}$ & $\begin{array}{r} 91 \\ \text { Pa } \\ \hline 231.04 \end{array}$ & $\begin{array}{c} 92 \\ \underline{U}-{ }_{238.03} \end{array}$ & $\begin{array}{c} 93 \\ \mathbf{N p} \\ {[237.05]} \end{array}$ & $\begin{array}{c} 94 \\ \frac{\mathrm{Pu}}{[244.06]} \end{array}$ & $\begin{array}{c} 95 \\ \mathrm{Am} \\ {[243.06]} \end{array}$ & $\begin{array}{c} 96 \\ \underline{[247.07} \end{array}$ \\ \hline \end{tabular} [3]

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Problem 303

Bob has 21 different dress shirts in his wardrobe. (a) In how many ways can Bob select seven shirts to pack for a business trip? (b) In how many ways can Bob select 5 of the 7 dress shirts he packed for the business trip? Each one is purposed for the five different events he will attend during the trip. (a) Bob can select seven shirts to pack for a business trip in $\square$ ways. (Simplify your answer.)

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Problem 304

How many dinner combinations can be made with 5 appetizers, 4 main courses, and 5 desserts?

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Problem 305

Keith must choose a shirt and a pair of pants for today's outfit. He has 3 shirts and 3 pairs of pants to choose from. How many different outfits can he make? $\square$

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Problem 306

What is the value of the expression? ${ }_{9} C_{3}$ 84 504 720 362,880

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Problem 307

8. How many rectangles can be made given six horizontal lines and five vertical lines?

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Problem 308

In how many different ways can six gold medals and four silver medals be distributed among ten athletes if each person is to receive one medal?

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Problem 309

Use the formula for ${ }_{n} \mathrm{P}_{\mathrm{r}}$ to evaluate the following expression. $\begin{array}{r} { }_{5} P_{3} \\ { }_{5} P_{3}= \end{array}$ $\square$

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Problem 310

Pytanie 7 Na ile sposobów można rozdać 20 identycznych czekoladek 8 dzieciom, tak że dokładnie troje z nich dostaje conajmniej 2 czekoladki? (2 punkty)

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Problem 311

4. In how many ways can 5 people be arranged in a line?

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Problem 312

How many electrons can be held in the $p$ subshell?

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Problem 313

Find arrangements of 5 letters from 'LANGSIR' starting with a vowel.

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Problem 314

2. How many ways can the letters of ALOHA be arranged if: a) the A's must be together? (2 marks)
AA $\qquad$ - $4!=24$ b) the A's cannot be together? (1 mark) $\qquad$ A $\qquad$ A $\qquad$ $3!=$ $\square$ 6 c) each arrangement must begin with a vowel and the consonants cannot be together? (2 marks) A.A. 0 L. H $\qquad$ $L H$

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Problem 315

1. A basketball team consists of some quards and six forwards. If there are 420 ways to select two guards and three forwards to the starting line-up, then the number of quards on the team is $\qquad$
2. A coach must choose the 5 starters for a basketball team from 6 males and 5 females. If there must be at least two of each gender in the starting line-up, the number of different groups of players that can be chosen is $\qquad$
3. A sports store has jerseys representing the seven Canadian NHL teams and the eight Canadian CFL teams. Five of these jerseys have to be chosen for display in a store window. The store owner decides to choose three NHL and two CFL jerseys. These jerseys will be arranged in a row in the store window. The number of displays that can be made by choosing the jerseys and then arranging them in the window is $\qquad$
4. How many arrangements of the word POPPIES can be made
If the first letter is $P$ and the next one is not $P$ .

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Problem 316

The lunch special at Maya's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 4 drinks, and 1 dessert to choose from. How many lunch specials are possible?

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Problem 317

The number of ways of arranging letters of word HAVANA such that $V$ and $N$ do not appear together is
Only one correct answer A. 20 B. 40 C. 80 D. 160

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Problem 318

Question 58: Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is
Only one correct answer A. 200 B. 350 C. 500 D. 300

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1 2 3 4

Combinatorics

Problem 301

Problem 302

Problem 303

Problem 304

How many dinner combinations can be made with 5 appetizers, 4 main courses, and 5 desserts?

Problem 305

Keith must choose a shirt and a pair of pants for today's outfit. He has 3 shirts and 3 pairs of pants to choose from. How many different outfits can he make? $\square$

Problem 306

What is the value of the expression? ${ }_{9} C_{3}$ 84 504 720 362,880

Problem 307

8. How many rectangles can be made given six horizontal lines and five vertical lines?

Problem 308

In how many different ways can six gold medals and four silver medals be distributed among ten athletes if each person is to receive one medal?

Problem 309

Use the formula for ${ }_{n} \mathrm{P}_{\mathrm{r}}$ to evaluate the following expression. $\begin{array}{r} { }_{5} P_{3} \\ { }_{5} P_{3}= \end{array}$ $\square$

Problem 310

Pytanie 7 Na ile sposobów można rozdać 20 identycznych czekoladek 8 dzieciom, tak że dokładnie troje z nich dostaje conajmniej 2 czekoladki? (2 punkty)

Problem 311

4. In how many ways can 5 people be arranged in a line?

Problem 312

How many electrons can be held in the $p$ subshell?

Problem 313

Find arrangements of 5 letters from 'LANGSIR' starting with a vowel.

Problem 314

Problem 315

Problem 316

The lunch special at Maya's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 4 drinks, and 1 dessert to choose from. How many lunch specials are possible?

Problem 317

The number of ways of arranging letters of word HAVANA such that $V$ and $N$ do not appear together is
Only one correct answer A. 20 B. 40 C. 80 D. 160

Problem 318

Question 58: Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is
Only one correct answer A. 200 B. 350 C. 500 D. 300

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Combinatorics

Problem 301

Problem 302

Problem 303

Problem 304

How many dinner combinations can be made with 5 appetizers, 4 main courses, and 5 desserts?

Problem 305

Keith must choose a shirt and a pair of pants for today's outfit. He has 3 shirts and 3 pairs of pants to choose from. How many different outfits can he make? □\square□

Problem 306

What is the value of the expression? 9C3{ }_{9} C_{3}9​C3​ 84 504 720 362,880

Problem 307

8. How many rectangles can be made given six horizontal lines and five vertical lines?

Problem 308

In how many different ways can six gold medals and four silver medals be distributed among ten athletes if each person is to receive one medal?

Problem 309

Use the formula for nPr{ }_{n} \mathrm{P}_{\mathrm{r}}n​Pr​ to evaluate the following expression. 5P35P3=\begin{array}{r} { }_{5} P_{3} \\ { }_{5} P_{3}= \end{array}5​P3​5​P3​=​ □\square□

Problem 310

Pytanie 7 Na ile sposobów można rozdać 20 identycznych czekoladek 8 dzieciom, tak że dokładnie troje z nich dostaje conajmniej 2 czekoladki? (2 punkty)

Problem 311

4. In how many ways can 5 people be arranged in a line?

Problem 312

How many electrons can be held in the ppp subshell?

Problem 313

Find arrangements of 5 letters from 'LANGSIR' starting with a vowel.

Problem 314

Problem 315

Problem 316

The lunch special at Maya's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 4 drinks, and 1 dessert to choose from. How many lunch specials are possible?

Problem 317

The number of ways of arranging letters of word HAVANA such that VVV and NNN do not appear together isOnly one correct answer A. 20 B. 40 C. 80 D. 160

Problem 318

Question 58: Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys AAA and BBB, who refuse to be the members of the same team, isOnly one correct answer A. 200 B. 350 C. 500 D. 300

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Keith must choose a shirt and a pair of pants for today's outfit. He has 3 shirts and 3 pairs of pants to choose from. How many different outfits can he make? $\square$

What is the value of the expression? ${ }_{9} C_{3}$ 84 504 720 362,880

Use the formula for ${ }_{n} \mathrm{P}_{\mathrm{r}}$ to evaluate the following expression. $\begin{array}{r} { }_{5} P_{3} \\ { }_{5} P_{3}= \end{array}$ $\square$

How many electrons can be held in the $p$ subshell?

The number of ways of arranging letters of word HAVANA such that $V$ and $N$ do not appear together is
Only one correct answer A. 20 B. 40 C. 80 D. 160

Question 58: Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $A$ and $B$ , who refuse to be the members of the same team, is
Only one correct answer A. 200 B. 350 C. 500 D. 300