Question 1202251: The number of committees consisting of 4 men and 5 women that can be formed from 10 men and 13 women is
Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! To form a committee of 4 men and 5 women from 10 men and 13women
4 men can be selected from 10 men in 10 C 4 ways
5 women can be selected from 13 women in 13C5ways
The total number of committees formed is
10C4 ×13C5 ways=210*1287
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
None of the seats on the committee have a label (eg: "president" or "treasurer"), which means order does not matter.
No member outranks another.
A group like {A,B,C} is the same as {B,C,A}.
Since order doesn't matter, we use the nCr combination formula.
Let's find out how many ways there are to select the men.
n = 10 men total
r = 4 men to select
n C r = (n!)/(r!(n-r)!)
10 C 4 = (10!)/(4!*(10-4)!)
10 C 4 = (10!)/(4!*6!)
10 C 4 = (10*9*8*7*6!)/(4!*6!)
10 C 4 = (10*9*8*7)/(4!)
10 C 4 = (10*9*8*7)/(4*3*2*1)
10 C 4 = 5040/24
10 C 4 = 210
There are 210 ways to select the four men from a candidate pool of ten men. Order doesn't matter.
nCr calculator
https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
This is one of many free online calculators that specialize in computing the nCr combination value.
If you have a TI84 or similar, then check out this example video.
https://www.youtube.com/watch?v=wxlJcZzJgpo
Coincidentally, the person goes over 10C4 = 210
The value 210 can be found in Pascal's Triangle.
Look at the row that starts with 1,10,...
Count 5 spaces to arrive at 210.
We count 5 spaces, and not 4, because the index starts at r = 0.
Use whichever method you prefer (calculator, formula, pascals triangle) to find that 13C5 = 1287 is the number of ways to pick the five women from a candidate pool of thirteen women.
Overall we have:
(10C4)*(13C5) = 210*1287 = 270270
ways to form this committee.
Answer: 270270
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