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

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.

If ""^(n)C_(r) denotes the number of combinations of n things taken r at a time, then the expression ""^(n)C_(r+1)+""^(n)C_(r-1)+2xx""^(n)C_(r) , equals

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 distinct permutations of the letters in MISSISSIPPI do the four I' s not come together?

Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time ?

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. In how many permutations does the first 0 precede the first 1 and the first 1 precede first 2 .