Eleven people, 7 men and 4 women, successfully completed their study at the School of Astronautics. A team of 6 people needs to be selected from them for the next intergalactic travel. In how many ways can 6 astronauts be selected, if at least 2 women and 3 men must be in the team�H

Question

This question was answered by Reiny and i was wondering how she got her andwer :
For at least 2 women and 3 men, the only cases would be
2W,4M = C(4,2) x C(7,4) = 6x35 = 210 , or
3W,3M = C(4,3) x C(7,3) = 4x35 = 140

for a total of 350 ways

I would like to know how you got the 35 in the 6 X 35 and the 4 X 35
Thank You
MathsHelpNeeded

Answer 1

Wow, this goes back quite some time.

by definition

C(n,r) = n!/(r!(n-r)!) , so
C(7,3) = 7!/(3!4!) = 35 , and
C(7,4) = 7!/(4!3!)

Most scientific calculators contain the functions C(n,r) and P(n,r)
they are probably written as _nC_r and _nP_r

Here is a page that explains the notation and difference between combination and permutation.

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

You might also google "Pascal's Triangle" to see a very interesting relationship between the values of C(n,r) and the rows of the triangle.

Look at the last row of this version of the triangle
http://mathforum.org/workshops/usi/pascal/images/fill.comb.gif