Question

Suppose you’re in a play where the grand finale requires 5 backup dancers. The

entire cast consists of 24 people (including yourself). If the order in which the backup dancers
are selected does not matter, then in how many ways can these dancers be chosen?

Answer 1

If the order in which the backup dancers are selected does not matter, we can use the combination formula to calculate the number of ways to choose 5 backup dancers from a group of 24 people.

The formula for combinations is:

n C r = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items to choose, and ! denotes the factorial function (the product of all positive integers up to a given number).

Plugging in the values for this problem, we get:

24 C 5 = 24! / (5! * (24-5)!)

Simplifying this expression:

24 C 5 = (24 * 23 * 22 * 21 * 20) / (5 * 4 * 3 * 2 * 1)

24 C 5 = 24,024

Therefore, there are 24,024 ways to choose 5 backup dancers from a group of 24 people if the order in which they are selected does not matter

Answer 2

42,504

Explanation:

When order matters, it is a permutation problem, and the answer is a bigger number.

When order does not matter, it is a combination problem, and the answer is a smaller number.

Since order does not matter, you need to calculate 24C5.

nCr = (n!)/[(n - r)!r!]

24C5 = (24!)/[(24 - 5)! × 5!]

24C5 = (24 × 23 × 22 × 21 × 20)/(5 × 4 × 3 × 2 × 1)

24C5 = 42,504