If p is a prime and if r ∈ N is such that 1≤ r ≤ p, then show that p devides PCг
rational:
are you really sure 1<=r<=p ?
shouldn't it be just 1<=r<p ?
because PCP = 1 and no integer divides 1
*no prime divides 1
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pCr = pC1 +pC2 + ...............................pCr
PCr = P!/(p-1) + P!/ (p-2)! ............P! /(p-r) !
p!/(p-r)= P!/(p-1)(p-2)(p-3).........(p-r)
p!/(p-r)=P! /P(p-1).......................
this shows that p divide PCr
PCr = P!/(p-1) + P!/ (p-2)! ............P! /(p-r) !
p!/(p-r)= P!/(p-1)(p-2)(p-3).........(p-r)
p!/(p-r)=P! /P(p-1).......................
this shows that p divide PCr
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