In how many ways can the letters of the word "CAPITAL" be arranged such that the vowels always remain together?

The sum of all four-digit numbers that can be formed with the distinct non-zero digits $$ a, b, c, $...

In how many distinct ways can the letters of the word "SMART" be arranged, given that all letters a...

A committee of 5 members is to be formed from a pool of 3 trainees, 4 professors, and 6 research as...

Six teachers are to stand in a row, where two are primary teachers, two are middle teachers, and tw...

From a group of 7 men and 6 women, a committee of 5 people must be formed such that the committee i...

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S a...