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Show that nCr=(n-r+1)/r.(nC(r-1))...

Show that `nC_r=(n-r+1)/r.(nC_(r-1))`

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Show that: .^nC_(n-r)+3.^nC_(n-r+1)+3.^nC_(n-r+2)+^nC_(n-r+3)=^(n+3)C_r .

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

Show that .^nC_r+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_r

Prove that nC_r = nC_(n-r)

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Show that ^nC_r+2. ^nC_(r-1)+ ^nC_(r-2)= ^(n+2)C_r

Prove that n.^(n-1)C_(r-1)=(n-r-1) ^nC_(r-1)

Prove that (""^nC_r)/(""^nC_(r-1))=(n-r+1)/r

Verify that ""^nC_r= frac (n)(r) "^(n-1)C_(r-1) and hence prove that "^nC_r= (n!)/(r!(n-r)!) .

Prove that ^"" nC_r=^nC_(n-r)