Question 1202251
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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
<a href="https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php">https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php</a>
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. 
<a href="https://www.youtube.com/watch?v=wxlJcZzJgpo">https://www.youtube.com/watch?v=wxlJcZzJgpo</a>
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: <font color="red" size=4>270270</font>
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