Question

At an awards ceremony, 5 women and 4 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

The first two awards are given to two of the women, and then the awards alternate between men and women. There are 100,800 ways this can be done.

Step-by-step explanation:

The first two awards are given to two of the five women, which can be done in 5P2 = 5 x 4 = 20 ways.

After that, the remaining awards will alternate between men and women. There are 3 remaining women and 4 men, so there are 7 individuals to choose from.

We can think of this as arranging the 3 women and 4 men in a line. The number of possible arrangements is 7P7 = 7!

Therefore, the total number of ways this can be done is 20 x 7! = 20 x 5040 = 100,800 ways.