[" Let "n" and "r" be non-negative integers "],[" such that "r<=n." Prove that: "],[^(n)C_(r)+^(n)C_(r-1)=^(n+1)C_(r)]

Let n and r be non negative integers such that 1<=r<=n* Then,^(n)C_(r)=(n)/(r)*^(n-1)C_(r-1)

Let n\ a n d\ r be non negative integers such that 1lt=rlt=ndot Then, \ ^n C_r=n/rdot\ \ ^(n-1)C_(r-1)\ dot

Let n and r be no negative integers suych that r<=n. Then,^(n)C_(r)+^(n)C_(r-1)=^(n+1)C_(r)

Let n\ a n d\ r be no negative integers suych that rlt=n .Then, \ ^n C_r+\ ^n C_(r-1)=\ ^(n+1)C_r

p, q and r are three non-negative integers such that p+q+r=10 . The maximum value of pq+qr+pr+pqr is

Notation + theorem :- Let r and n be the positive integers such that 1<=r<=n. Then no.of all permutations of n distinct things taken r at a time is given by (n)(n-1)(n-2)....(n-(r-1))

If n is a positive integer and r is a nonnegative integer, prove that the coefficients of x^r and x^(n-r) in the expansion of (1+x)^(n) are equal.