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Question Number 74337 by Maclaurin Stickker last updated on 22/Nov/19
findthecontractedformof:(np)+2(np+1)+(np+2)
Answered by MJS last updated on 23/Nov/19
(np)=n!p!(n−p)!=n!(p+1)(p+2)p!(n−p)!(p+1)(p+2)2(np+1)=2n!(p+1)!(n−p−1)!=2n!(n−p)p!(n−p)!(p+1)==2n!(n−p)(p+2)p!(n−p)!(p+1)(p+2)(np+2)=n!(p+2)!(n−p−2)!==n!(n−p)(n−p−1)p!(n−p)!(p+1)(p+2)(np)+2(np+1)+(np+2)==n!((p+1)(p+2)+2(n−p)(p+2)+(n−p)(n−p−1))p!(n−p)!(p+1)(p+2)==n!(n2+3n+2)p!(n−p)!(p+1)(p+2)==n!(n+1)(n+2)p!(n−p)!(p+1)(p+2)=(n+2)!(p+2)!(n−p)!==(n+2)!(p+2)!((n+2)−(p+2))!=(n+2p+2)
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