Q. 20 C5.0( 2 Votes )

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

Class 11th RD Sharma - Mathematics 17. Combinations

Answer :

Given that we need to prove

Consider L.H.S,

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

= R.H.S

∴ L.H.S = R.H.S, thus proved.

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PREVIOUSLet r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:n.n – 1Cr – 1 = (n – r + 1)(nCr – 1)NEXTLet r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:nCr + 2nCr – 1 + nCr – 2 = n + 2Cr

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