Calculate the number of permutations nPr and combinations nCr for any n and r up to n = 170.
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From the article Permutation vs Combination â Deciding nPr or nCr in Five Seconds.
(a) From 10 students, a committee of 3 is to be formed. In how many ways?
Swapping two committee members changes nothing â it is the same committee. Order does not matter, so use nCr:
10C3 = (10 Ă 9 Ă 8) / (3 Ă 2 Ă 1) = 720 / 6 = 120 ways
(b) From the same 10 students, a president, a secretary and a treasurer are to be chosen. In how many ways?
Now swapping two of them does change the outcome â a different person is president. Order matters, so use nPr:
10P3 = 10 Ă 9 Ă 8 = 720 ways
The relationship, confirmed: 720 = 120 Ă 3! = 120 Ă 6 â Each of the 120 committees can hand out the three posts in 6 different ways.
Worked in full in Permutation vs Combination â Deciding nPr or nCr in Five Seconds.
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