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

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

The number of circular permutations of 8 things taken 4 at a time is

The number of circular permutation of 8 things taken 4 at a time is

The number of circular permutations of 8 things taken 4 at a time is

The no.of all permutation of n distinct things taken all at a time is n!

2.The number of permutations of 8 things taken at a time is 1680, Then r=

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

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)