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Home / Aptitude Tests / Further Mathematics / Simplify: \(^{n}C_{r...
Simplify: nCr÷nCr1...

Simplify: nCr÷nCr1

A.

n(nr)r

B.

nr(nr)

C.

1r(nr)

D.

n+1rr

Correct answer is D

nCr=n!(nr)!r!

nCr1=n!(n(r1))!(r1)!

nCr÷nCr1=n!(nr)!r!÷n!(n(r1))!(r1)!

= n!(nr)!r!×(n(r1)!(r1)!n!

= (n+1r)!(r1)!(nr)!r!

= (n+1r)(nr)!(r1)!(nr)!r(r1)!

= n+1rr