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March 27, 2017

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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 teamĀH

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 - ,

    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 nCr and nPr

    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

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