A committee of six is chosen from 14 people. In how many ways can this be done?

This is a combination problem. The formula for combinations is:

C(n, k) = n! / [k!(n-k)!]

where:

• n is the total number of options,
• k is the number of options chosen at a time,
• "!" denotes factorial, which means multiplying all positive integers up to that number.

In this case, n = 14 (the total number of people) and k = 6 (the number of people to choose for the committee).

So, the number of ways to choose a committee of six from 14 people is:

C(14, 6) = 14! / [6!(14-6)!]

Calculating the factorials:

14! = 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 6! = 6 × 5 × 4 × 3 × 2 × 1 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Substituting these into the formula gives:

C(14, 6) = (14 × 13 × 12 × 11 × 10 × 9) / (6 × 5 × 4 × 3 × 2 × 1)

Calculating this gives:

C(14, 6) = 3003

So, there are 3003 ways to choose a committee of six from 14 people.