Find the smallest number which leaves remainder 1,2 and 3 when divided by 11,13 and 17.
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Sol:
Given 2nCn = (2n)! / n! n!
= (2n)! / (n!)2
= (2n) ( 2n - 1) (2n - 2) -----------4.3.2.1 / (n!)2
= 2xn ( 2n - 1) 2 ( n - 1) -----------------2x2.3.2x1.1 / (n!)2
= 2n [n(n - 1)(n - 2)(n -3) ----------3 x2 x1][(2n -1)(2n -3) ---------------5x3x1] / (n!)2
= 2n n! [(2n -1)(2n -3) ---------------5x3x1] / (n!)2
= 2n [(2n -1)(2n -3) ---------------5x3x1] / (n!)
= 2n[ 1x3x5 -----------------(2n -3)(2n -1)] / (n!)
Step-by-step explanation:
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