from a group of women and 4 men, determine in how many ways a committee of people can be selected with no restrictions?

b. 4 women
c. 3 women and 1 men
d. 2 women 2 man
e. 4 men

<from a group of women and 4 men...>

did you forget to tell us how many women there are?

Is this this correct. 0.01%=0.01 because in 0.01% the percent is already written as a decimal

To determine the number of ways a committee can be selected with no restrictions, we need to calculate the combinations. The formula to calculate the combination is:

C(n, k) = n! / (k!(n-k)!)

Where:
- n is the total number of people (in this case, the group of women and men).
- k is the number of people to be selected for the committee.

Let's solve each part of the question.

b. 4 women:
Since there are only 4 men, we need to select all 4 women from the group. Therefore, the number of ways to select the committee would be:

C(4+4, 4) = C(8, 4) = 8! / (4!(8-4)!) = 8! / (4!4!) = 70

So there are 70 ways to select a committee with 4 women.

c. 3 women and 1 man:
In this case, we need to select 3 women from the group of women and 1 man from the group of men. Therefore, the number of ways to select the committee would be:

C(4, 3) * C(4, 1) = (4! / (3!(4-3)!)) * (4! / (1!(4-1)!)) = 4 * 4 = 16

So there are 16 ways to select a committee with 3 women and 1 man.

d. 2 women and 2 men:
Similar to the previous case, we need to select 2 women from the group of women and 2 men from the group of men. Therefore, the number of ways to select the committee would be:

C(4, 2) * C(4, 2) = (4! / (2!(4-2)!)) * (4! / (2!(4-2)!)) = 6 * 6 = 36

So there are 36 ways to select a committee with 2 women and 2 men.

e. 4 men:
If we want to select only 4 men, we don't need to consider the women in this case since there are no restrictions. Therefore, the number of ways to select the committee would be:

C(4, 4) = 4! / (4!(4-4)!) = 1

So there is 1 way to select a committee with 4 men.

In summary:
b. 4 women: 70 ways
c. 3 women and 1 man: 16 ways
d. 2 women and 2 men: 36 ways
e. 4 men: 1 way