Permutations#!#Formula P(n,r)

In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is ""^(n-m)P_(r-m)xx""^(r)P_(m) .

The number of permutations of n different things taking r at a time when 3 particular things are to be included is ^(n-3)P_(r-3) b.n-3P_(r) c.^(n)P_(r-3) d.r!^(n-3)C_(r-3)

Let ."""^(n)P_(r) denote the number of permutations of n different things taken r at a time . Then , prove that 1+1."""^1P_(1) + 2 ."""^(2)P_(2) + 3."""^(3)P_(3) +.....+ n . """^(n)P_(n) = . """^(n+1)P_(n+1)

If P(n, n) denotes the number of permutations of n different things taken all at a time then P(n, n) is also identical to , where 0 le r le n

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 the no.of all permutations of n different objects taken r at a time when a particular object is to be always included in each arrangement is r.(n-1)P_(r-1)

Prove that the no.of permutations of n different objects taken r at a time in which two specified objects always occur together 2!(r-1)(n-2)P_(r-2)

The number of permutations of n different objects taken r(>=3) at a time which include 3 particular objects is

(i) If the number of permutations of n different thing taken r at a time be denoted by (nPr) Show that,