An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. In how many ways can the awards alternate between men and women with the first award being presented to a woman

The following option is not correct:

(a) If 100 numbers are generated comma each integer between 0 and 99 must occur exactly once.

Step-by-step explanation:

This is not correct, as there is a possibility of an integer being generated twice when 100 numbers are generated.

This can be explained with an example such as stated below:

3 numbers are to be generated.

The number generated can either be 1, 2, or 3.

The probability for all three numbers to be generated once when the generator is run 3 times is:

(1/3)*(1/3)*(1/3) * Number of ways to arrange the three numbers

Thus this probability will be:

Probability = (1/3)^3 * 3!

Probability = 0.222

Since the probability here is not equal to 1, the probability for the same thing happening at a larger scale will also not be 1.