Is ^nCr = ^nCn-r true?(a) True(b) FalseI had been asked this question at a job interview.The doubt is from Combinations in chapter Permutations and Combinations of Mathematics – Class 11

Is ^nCr = ^nCn-r true?(a) True(b) FalseI had been asked this question

1.	Is ^nCr = ^nCn-r true?(a) True(b) FalseI had been asked this question at a job interview.The doubt is from Combinations in chapter Permutations and Combinations of Mathematics – Class 11
Answer» Right CHOICE is (a) True The explanation: We know, ^NCR = \(\frac{N!}{(n-r)! r!}\). REPLACING r by n-r, we get ^nCn-r = \(\frac{n!}{(n-(n-r))!(n-r)!} = \frac{n!}{r! (n-r)!}\) = ^nCr => ^nCr = ^nCn-r

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