Question

At an awards ceremony, nine women and seven men are each to receive an award and are to be presented with their award one at a time. Two of the awards are to be first given to two of the women, and then the remaining awards will alternate between men and women. How many ways can this be done

Answer 1

Answer:

3432 different ways.

Step-by-step explanation:

Since the men and women are not individually characterized (no names are given) we will treat them as similar objects with regards to permutations.

Let's leave out the two women that receive the award first.

We now have 7 men and 7 women to receive the reward.

This translates to the following permutation:

$\frac{14!}{7!*7!}$ = 3432 different ways to give out the awards.

The 7! in the denominator exist to account for same objects, 7! for men and 7! for women.