Use these filters to find papers

Question

10
requests

(a) If nPr=npr+1, and nCr=nCr-1_, then find n and r.


Answers

  • 0

    ⁿPr=ⁿPr+1

    or, n!/(n-r)!=n!/(n-r-1)!

    or, n!/(n-r)(n-r-1)!=n!/(n-r-1)!

    or, 1/(n-r)=1

    or, n-r=1 ------------------(1)

    Again,

    ⁿCr=ⁿCr-1

    or, n!/r!(n-r)!=n!/(r-1)!(n-r+1)!

    or, 1/r(r-1)!(n-r)!=1/(r-1)!(n-r+1)(n-r)!

    or, 1/r=1/(n-r+1)

    or, r=n-r+1

    or, n-2r=-1 --------------------(2)

    Subtracting (2) from (1) we get,

    n-n-r+2r=1+1

    or, r=2

    Putting in (1),

    n-2=1

    or, n=3

    ∴, n=3, r=2

    Answerd on November 2019 by
    User Image
Write an answer for this question
Preview