NIMCET 2014 — Mathematics PYQNIMCET | Mathematics | 2014If n and r are integers such that 1≤r≤n, then the value of n(n−1Cr−1) is:Ask AI TutorChoose the correct answer:A. nCrB. r(nCr) (Correct Answer)C. n(nCr)D. (n−1)(nCr)Correct Answer: r(nCr)Explanation X=n(n−1Cr−1) X=n((r−1)!×((n−1)−(r−1))!(n−1)!) X=(r−1)!×(n−r)!n×(n−1)! X=(r−1)!×(n−r)!n! Multiply r to numerator and denominator: X=(r×(r−1)!)×(n−r)!r×n! X=r(r!×(n−r)!n!) X=r(nCr) AnCrBr(nCr)Cn(nCr)D(n−1)(nCr)Show Answer SExplanation X=n(n−1Cr−1) X=n((r−1)!×((n−1)−(r−1))!(n−1)!) X=(r−1)!×(n−r)!n×(n−1)! X=(r−1)!×(n−r)!n! Multiply r to numerator and denominator: X=(r×(r−1)!)×(n−r)!r×n! X=r(r!×(n−r)!n!) X=r(nCr)
