If `^nP_4=12xx ^nP_2`, find n.

If ^nP_3=9240 , find n

If "^nP_4: ^(n+1)P_4=3:4 , find n.

If nP5=20nP3 find the value of n

If .^nP_r=840, .^nC_r=35, then find n=

If C(n,4) = C(n,6). Find C(12,n)

Prove that nP_n=2 ^nP_(n-2)

Let A={1,2,..., n} and B={a , b }. Then number of surjections from A into B is nP2 (b) 2^n-2 (c) 2^n-1 (d) nC2

Let A={1,2,..., n} and B={a , b }. Then number of surjections from A into B is nP2 (b) 2^n-2 (c) 2^n-1 (d) nC2

If ^nP_(r-1):^nPr: ^nP_(r+1)=a,b:c, prove that b^2=a(b+c)

If A={x:x=3n,n in N} and B={x:x=4n,n in N} , then find A cap B .