Question

Circle the correct choice. Identify n and k, and substitute these

into the correct formula. You do not need to simplify.

3. There are 100 people at a basketball game. 10 winners are chosen. Each winner wins an identical team T-shirt. To find the number of ways to choose the winners, you use (permutations/combinations).

There are 30 students in a club. The club chooses a president, Vice president, and secretary. To find the number of ways to choose the officers, you use (permutations/combinations)

(-help I don’t get it)

Answer 1

3. To find the number of ways to choose the winners, you use combinations.

n = 100 (total number of people)

k = 10 (number of winners to be chosen)

The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Substituting n and k into the formula, we get:

C(100,10) = 100! / (10! * (100-10)!)

We do not need to simplify this expression.

For the club with 30 students, the number of ways to choose the officers is given by permutations because the order in which the officers are chosen matters.

n = 30 (total number of students)

k = 3 (number of officers to be chosen)

The formula for permutations is:

P(n,k) = n! / (n-k)!

Substituting n and k into the formula, we get:

P(30,3) = 30! / (30-3)!

We do not need to simplify this expression.