Math / Discrete

QuestionGJU-Elearning My Classes English (en) Dashboard Courses All Courses School of Applied Technical Sciences First Semester 2024/2025 IE0121:Probability and Statistics-2024 First Section 3 General First Preview
Tomorrow is election day for university students representatives. Let us assume that 22 students in your university are candidates for this election. From these 22 students, a president, two vice-presidents, and two president assistants will be filled. In how many different ways can the offices be filled? 790020 3160080 1580040 1053360 Clear my choice

Studdy Solution

STEP 1

1. The positions of president, vice-presidents, and president assistants are distinct.
2. Once a student is chosen for a position, they cannot be chosen for another position.
3. The order in which students are chosen for positions matters.

STEP 2

1. Determine the number of ways to choose the president.
2. Determine the number of ways to choose the two vice-presidents.
3. Determine the number of ways to choose the two president assistants.
4. Calculate the total number of ways to fill all positions.

STEP 3

First, choose the president. There are 22 students available, so there are 22 ways to choose the president.

STEP 4

After choosing the president, 21 students remain. Choose the first vice-president. There are 21 ways to choose the first vice-president.

STEP 5

After choosing the first vice-president, 20 students remain. Choose the second vice-president. There are 20 ways to choose the second vice-president.

STEP 6

After choosing the two vice-presidents, 19 students remain. Choose the first president assistant. There are 19 ways to choose the first president assistant.

STEP 7

After choosing the first president assistant, 18 students remain. Choose the second president assistant. There are 18 ways to choose the second president assistant.

STEP 8

Multiply the number of ways to fill each position to find the total number of ways to fill all positions:
$22 \times 21 \times 20 \times 19 \times 18$

STEP 9

Calculate the product:
$22 \times 21 \times 20 \times 19 \times 18 = 3160080$
The number of different ways to fill the offices is:
$\boxed{3160080}$

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Studdy Solution

STEP 1

1. The positions of president, vice-presidents, and president assistants are distinct.
2. Once a student is chosen for a position, they cannot be chosen for another position.
3. The order in which students are chosen for positions matters.

STEP 2

1. Determine the number of ways to choose the president.
2. Determine the number of ways to choose the two vice-presidents.
3. Determine the number of ways to choose the two president assistants.
4. Calculate the total number of ways to fill all positions.

STEP 3

First, choose the president. There are 22 students available, so there are 22 ways to choose the president.

STEP 4

After choosing the president, 21 students remain. Choose the first vice-president. There are 21 ways to choose the first vice-president.

STEP 5

After choosing the first vice-president, 20 students remain. Choose the second vice-president. There are 20 ways to choose the second vice-president.

STEP 6

After choosing the two vice-presidents, 19 students remain. Choose the first president assistant. There are 19 ways to choose the first president assistant.

STEP 7

After choosing the first president assistant, 18 students remain. Choose the second president assistant. There are 18 ways to choose the second president assistant.

STEP 8

Multiply the number of ways to fill each position to find the total number of ways to fill all positions:
$22 \times 21 \times 20 \times 19 \times 18$

STEP 9

Calculate the product:
$22 \times 21 \times 20 \times 19 \times 18 = 3160080$
The number of different ways to fill the offices is:
$\boxed{3160080}$

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Studdy Solution

STEP 1

1. The positions of president, vice-presidents, and president assistants are distinct.2. Once a student is chosen for a position, they cannot be chosen for another position.3. The order in which students are chosen for positions matters.

STEP 2

1. Determine the number of ways to choose the president.2. Determine the number of ways to choose the two vice-presidents.3. Determine the number of ways to choose the two president assistants.4. Calculate the total number of ways to fill all positions.

STEP 3

First, choose the president. There are 22 students available, so there are 22 ways to choose the president.

STEP 4

After choosing the president, 21 students remain. Choose the first vice-president. There are 21 ways to choose the first vice-president.

STEP 5

After choosing the first vice-president, 20 students remain. Choose the second vice-president. There are 20 ways to choose the second vice-president.

STEP 6

After choosing the two vice-presidents, 19 students remain. Choose the first president assistant. There are 19 ways to choose the first president assistant.

STEP 7

After choosing the first president assistant, 18 students remain. Choose the second president assistant. There are 18 ways to choose the second president assistant.

STEP 8

Multiply the number of ways to fill each position to find the total number of ways to fill all positions:22×21×20×19×18 22 \times 21 \times 20 \times 19 \times 18 22×21×20×19×18

STEP 9

Calculate the product:22×21×20×19×18=3160080 22 \times 21 \times 20 \times 19 \times 18 = 3160080 22×21×20×19×18=3160080 The number of different ways to fill the offices is:3160080 \boxed{3160080} 3160080​

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Studdy solves anything!

Start learning now

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

1. The positions of president, vice-presidents, and president assistants are distinct.
2. Once a student is chosen for a position, they cannot be chosen for another position.
3. The order in which students are chosen for positions matters.

1. Determine the number of ways to choose the president.
2. Determine the number of ways to choose the two vice-presidents.
3. Determine the number of ways to choose the two president assistants.
4. Calculate the total number of ways to fill all positions.

Multiply the number of ways to fill each position to find the total number of ways to fill all positions:
$22 \times 21 \times 20 \times 19 \times 18$

Calculate the product:
$22 \times 21 \times 20 \times 19 \times 18 = 3160080$
The number of different ways to fill the offices is:
$\boxed{3160080}$