In how many permutations of 11 dissimilar things, taken 4 at a time, will one particular thing always occur?

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

If a denotes the number of permutations of x + 2 things taken all at a time, b denotes the number of permutations of x things taken 1 1 at a time and c denotes the number of permutations of x - 1 1 things taken all at a time such that a = 182 be, then the value of x is

If six times the number of permutations of n things taken 3 at a time is equal to seven times the number of permutations of (n-1) things chosen 3 at a time, find n.

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object. (a) always occurs (b) never occurs.

A round table conference is to be held between 20 delegates and 20 countries. In how many ways can they be seated if two particular delegates are always to sit together?

How many numbers can be formed with the digits 3, 4, 6, 7, 8 taken all at a time ? Find the sum of all such numbers.