Math / Discrete

QuestionGiven the experiment, determine the number of outcomes possible 5 different states from the United States of America are chosen.

Studdy Solution

STEP 1

1. There are 50 states in the United States of America.
2. The order in which the states are chosen does not matter.
3. Each state can only be chosen once.

STEP 2

1. Identify the type of combinatorial problem.
2. Use the combination formula.
3. Calculate the number of combinations.

STEP 3

Identify the type of combinatorial problem:
This is a combination problem because the order of selection does not matter, and we are choosing a subset from a larger set.

STEP 4

Use the combination formula:
The formula for combinations is given by:
$C(n, r) = \frac{n!}{r!(n-r)!}$
where $n$ is the total number of items to choose from, and $r$ is the number of items to choose.

STEP 5

Calculate the number of combinations:
Substitute $n = 50$ and $r = 5$ into the formula:
$C(50, 5) = \frac{50!}{5!(50-5)!}$
Calculate the factorials:
$C(50, 5) = \frac{50 \times 49 \times 48 \times 47 \times 46}{5 \times 4 \times 3 \times 2 \times 1}$
Calculate the result:
$C(50, 5) = \frac{254251200}{120} = 2118760$
The number of possible outcomes when choosing 5 different states is:
$\boxed{2118760}$

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