Prove that ` nP_2= ^nP_(n-2) `

11. Prove that nP_(r)=n(n-1)P_(r-1)

Prove that P(n;r)=nP_(r)=n(!)/(n-r)!

prove that 1P_(1)+2.2P_(2)+3.3P_(3)+.......+n.nP_(n)=(n+1)P_(n+1)-1

If P_(m) stands for mP_(m), then prove that: 1+1.P_(1)+2.P_(2)+3.P_(3)+...+n.P_(n)=(n+1)!

Let nP_(r) denote the number of permutations of n differenttaken r at a time.Then,prove that 1+1*1P_(1)+2*2P_(2)+3*3P_(3)+......+n*nP_(n)=n+1P_(n+)

Prove that: 1.P (1,1)+2.P(2,2)+3.P(3,3)+...+n.P(n,n)=P(n+1,n+1)-1

If the number of permutations of n different things taken r at a time be denoted by nP_(r) show that (nP_(1))/(1!)+(nP_(2))/(2!)+(nP_(3))/(3!)+......+(nP_(n))/(n!)=2^(n)-1

Find the value of n such that (i)^nP_(5)=42^(n)P_(3),n>4(nP_(4))/(n-1P_(4))=(5)/(3),n>4

Show that ^(^^)nP_(r)=(n-r+1)^(n)P_(r-1)

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