Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

The number of permutations of n things taken r at a time if 3 particular things always occur is

Find the number of permutations of n different things taken r at a time such that two specific things occur together?

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) .

STATEMENT-1 :The total number of combinations of n thing by taking some or all is 2^(n) . STATEMENT -2 : 5 identical balls can be distributed among 10 identical boxes in only one way if not more than one ball can go into a box. STATEMENT-3 : In the permutations of n things taken r at a time , the number of permutations in which m particular things occur together is ""^(n - m)P_(r - m) * ""^(r)P_(m)

Prove that the number of combinations of n things taken r at a time in which p particular things always occur is .^(n-p)C_(r-p)

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

Find the total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times.

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)

There are 4n things of which n are alike and the rest different. Find the number of permutations of 4n things taken 2n at a time, each permutation containing the n like things.

Show that the total number of permutations of n different things taken not more than r at a time, when each thing may be repated any number of times is (n(n^(r)-1))/((n-1)) .