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# Permutation and Combination.

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There are 24 Persons (p1,p2,p3,......) from which a team of 12 Persons has to be made. p1 and p2 can only come together in the team. p3 and p4 can never come together in the team. In how many ways can the team be formed?
Guest Jan 17, 2016
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There are 24 Persons (p1,p2,p3,......) from which a team of 12 Persons has to be made. p1 and p2 can only come together in the team. p3 and p4 can never come together in the team. In how many ways can the team be formed?

If there were no restrictions at all then there would be  24C12 = 2,704,156 ways.

It has to be a lot less then that

This is what I am thinking.

Say we take those 4 out and deal with them seperately.  Then we will only be chosing from 20 people

P1 and P2 are  chosen,  P3 is chosen and P4 is NOT chosen           3 in aready             20C9

P1 and P2 are  chosen,  P3 is NOT chosen and P4 is chosen           3 in aready             20C9

P1 and P2 are  chosen,  P3 is NOT chosen and P4 is NOT chosen    2 in already           20C10

P1 and P2 are  NOT chosen,  P3 is chosen and P4 is NOT chosen        1 in already          20C11 = 20C9

P1 and P2 are  NOT chosen,  P3 is NOT chosen and P4 is chosen      1 in already          20C11 = 20C9

P1 and P2 are  NOT chosen,  P3 is NOT chosen and P4 is NOT chosen  0 in already      20C12

20C9+20C9+10C10+10C9+20C9+20C12 = 4 * 20C9 +  20C10 + 20C12

These are the possibilities4*nCr(20,9)+nCr(20,10)+nCr(20,12) = 982566

So I think that there are  982,566 possible choices.    ://

Melody  Jan 17, 2016

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