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.

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?

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

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

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

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

In how many of the permutations of n thing taken r at a time will three given things occur?

In how many of the permutations of n thing taken r at a time will three given things occur?

If a denotes the number of permutations of (x+2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things taken all at a time such that a=182b c , find the value of xdot

If a denotes the number of permutations of (x+2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things taken all at a time such that a=182b c , find the value of xdot