Posted by MathsHelpNeeded on Thursday, August 27, 2009 at 6:34am.
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 teamĀH
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

Maths  Reiny, Thursday, August 27, 2009 at 8:03am
Wow, this goes back quite some time.
by definition
C(n,r) = n!/(r!(nr)!) , 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 _{n}C_{r} and _{n}P_{r}
Here is a page that explains the notation and difference between combination and permutation.
http://www.mathsisfun.com/combinatorics/combinationspermutations.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
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