Latest TCS Aptitude Question SOLUTION: What is ∑K=028K2(28KC) where 28KC is the number of ways of choosing k items from 28 items?

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What is ∑K=028K2(28KC) where 28KC is the number of ways of choosing k items from 28 items?

Asked In TCS pre (10 years ago)

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prashant sharma  (10 years ago)

Consider (1+x)n=C0+C1x+C2x2+.....+Cnxn .......(1)
Differentiating w.r.t x we get
n(1+x)n−1=C1+2C2x+3C3x2+.....+nCnxn−1
Multiplying by x on both sides,
x.n(1+x)n−1=x.C1+2C2x2+3C3x3+.....
Now again differentiating w.r.t to x
n(1+x)n−1+n(n−1)x(1+x)n−2=C0+22C1x+32C2x2+42C3x3.....
Putting x = 1, we get
n(n+1)2n−2=C1+22C2+32C3+42C4
Now substituting n = 28
28(28+1)228−2 = 812.226 = 406.227

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