An executive committee consists of 13 members: 6 men and 7 women. 5 members are selected at random to attend a meeting in Hawail. The names are drawn from a hat. What is the probability that all 5 selected are men? The probability that all selected are men is (Simplify your answer. Type an integer or a simplified fraction)

Answer:

To distribute 32,400 pairs of sunglasses evenly among X people, we need to find the positive integer values of X that divide 32,400 without any remainder.

To determine the values of X for which this is possible, we can iterate through the positive integers from 10 to 180 and check if 32,400 is divisible by each integer.

Let's calculate:

Number of possible values for X = 0

For each value of X from 10 to 180, we check if 32,400 is divisible by X using the modulo operator (%):

for X = 10:

32,400 % 10 = 0 (divisible)

for X = 11:

32,400 % 11 = 9 (not divisible)

for X = 12:

32,400 % 12 = 0 (divisible)

...

for X = 180:

32,400 % 180 = 0 (divisible)

We continue this process for all values of X from 10 to 180. If the remainder is 0, it means that 32,400 is divisible by X.

In this case, the number of possible values for X is the count of the integers from 10 to 180 where 32,400 is divisible without a remainder.

After performing the calculations, we find that 32,400 is divisible by the following values of X: 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180.

Therefore, there are 33 possible values for X between 10 and 180 (inclusive) for which it is possible to distribute 32,400 pairs of sunglasses evenly.

Hope it helps!