Question

There are 6 boys and 6 girls in the finals of a talent contest. A contest is held to pick the top 3 winners in both the boy and girl groups in order of talent. How many different options for winners are there?

Options:
A. 12,200
B. 32,000
C. 14,400
D. 27,000

Answer 1

The number of different options for winners in the talent contest is 400.

Step-by-step explanation:

In order to determine the number of different options for winners in the talent contest, we need to calculate the number of ways to select 3 winners from a group of 6 boys and 3 winners from a group of 6 girls. This can be done using the combination formula. The formula for calculating combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of options and r is the number of options to be chosen. Using this formula, we can calculate:

C(6, 3) * C(6, 3) = (6! / (3!(6-3)!)) * (6! / (3!(6-3)!)) = (6 * 5 * 4) / (3 * 2 * 1) * (6 * 5 * 4) / (3 * 2 * 1) = 20 * 20 = 400

Therefore, the number of different options for winners in the talent contest is 400.