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If n(>=3) is a +ve integer,then value of the expression (n-3)Cr+3*(n-3)C(r-1) +3*(n-3)C(r-2)+(n-3)C(r-3) is (a)(n-2)Cr (b) (n-1)Cr (c)nCr (d)(n+1)Cr

If n(>=3) is a +ve integer,then value of the expression (n-3)Cr+3*(n-3)C(r-1)
+3*(n-3)C(r-2)+(n-3)C(r-3) is
(a)(n-2)Cr
(b) (n-1)Cr
(c)nCr
(d)(n+1)Cr

Grade:12

1 Answers

Pratham Ashish
17 Points
12 years ago

Dear Vaibhav,

dis problem is very straight forward , here u just hav to use nCr + nC(r-1) = (n+1)Cr

now just expand the terms and apply the above formula and combine two terms to get a single term ,the result wud be

(n-2)Cr + (n-2)C(r-2) + (n-2)C(r-1)+ (n-2)C(r-1)

again apply d same formula and u will get

(n-1)Cr + (n-1)C(r-1)

and finally

nCr hence ans = (c)

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