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There are 3 women and 8 men signed up to join a swing dance class. In how many ways can the instructor choose 4 of the people to join if more than 1 must be men?(If necessary, consult a list of formulas.)

Question

There are 3 women and 8 men signed up to join a swing dance class. In how many ways can the instructor choose 4 of the people to join if more than 1 must be men?(If necessary, consult a list of formulas.)

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Solution

To solve this problem, we need to use the combination formula which is C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose.

First, let's consider the different scenarios:

  1. Choosing 3 men and 1 woman
  2. Choosing 2 men and 2 women
  3. Choosing 1 man and 3 women
  4. Choosing 4 men

For each scenario, we calculate the number of combinations:

  1. Choosing 3 men and 1 woman: C(8,3) * C(3,1) = 56 * 3 = 168
  2. Choosing 2 men and 2 women: C(8,2) * C(3,2) = 28 * 3 = 84
  3. Choosing 1 man and 3 women: C(8,1) * C(3,3) = 8 * 1 = 8
  4. Choosing 4 men: C(8,4) = 70

However, the problem states that more than 1 man must be chosen, so we exclude the third scenario.

So, the total number of ways the instructor can choose 4 people with more than 1 man is 168 + 84 + 70 = 322.

This problem has been solved

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