SOLUTION: 1. how many ways can a jury of 9 men and 3 women be selected from 15 men and 11 women?

Question 341424: 1. how many ways can a jury of 9 men and 3 women be selected from 15 men and 11 women?
Found 2 solutions by Theo, solver91311:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
You want a jury of 9 men and 3 women.

Your universe is 15 men and 11 women.

the 9 men can chosen in 15! / (9! * 6!) ways.

The 3 women can be chosen in 11! / (3! * 8!) ways.

The total possible ways would be the result of multiplying both of those together.

You should get 5005 * 165 = 825825 ways.

To see how this works, use much smaller numbers.

Assume you want a jury of 2 men and 1 woman out of a universe of 3 men and 2 women.

The number of ways you can get 2 men from 3 men is 3! / (2! * 1!).

The number of ways you can get 1 woman from 2 women is 2! / (1! * 1!).

The 2 men can be chosen in 3 ways.

The 1 woman can be chosen in 2 ways.

The total number of ways would then be equal to 3 * 2 = 6.

Let your men be a, b, and c.

Let your women be w and x

Your possible combinations for the men are:

ab
ac
bc

Your possible combinations for the women are:

w
x

Your jury can consist of:
abw
acw
bcw

abx
acx
bcx

The formula works for this very small number.

Raise your numbers a little to see if the formula still works.

You want 3 men out of 5 men.
You want 2 women out of 4 women.

The number of ways you can get the men are equal to 5! / (3! * 2!).

the number of ways you can get the women are equal to 4! / (2! * 2!).

The number of ways to get the men is equal to 10.

The number of ways to get the women is equal to 6.

the total number of ways should be equal to 10 * 6 = 60.

Let's see if that works.

Let your men be a,b,c,d,e

Let your women be w,x,y,z

the possible combinations for your men are:

abc
abd
abe
acd
ace
ade
bcd
bce
bde
cde

The possible of ways for your women are:

wx
wy
wz
xy
xz
yz

the total possible combinations for the jury are:

10 possible combinations of men for each of the 6 possible combinations of women which equals a total of 60 possible comnbinations, none of which contain all members that are the same as all members in any other combination.

Those combinations are:

abcwx
abdwx
abewx
acdwx
acewx
adewx
bcdwx
bcewx
bdewx
cdewx

abcwy
abdwy
abewy
acdwy
acewy
adewy
bcdwy
bcewy
bdewy
cdewy

abcwz
abdwz
abewz
acdwz
acewz
adewz
bcdwz
bcewz
bdewz
cdewz

abcxy
abdxy
abexy
acdxy
acexy
adexy
bcdxy
bcexy
bdexy
cdexy

abcxz
abdxz
abexz
acdxz
acexz
adexz
bcdxz
bcexz
bdexz
cdexz

abcyz
abdyz
abeyz
acdyz
aceyz
adeyz
bcdyz
bceyz
bdeyz
cdeyz

Since the formula works with the smaller universe, you can be reasonably sure that it will work with a larger universe as well.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Calculate:

Where is the number of combinations of things taken at a time and is calculated by

John

My calculator said it, I believe it, that settles it

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