List of top Quantitative Aptitude Questions on permutations and combinations

The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is

A family consists of a grandfather, 5 sons and daughters and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is

If \({}^nC_x=56\) and \({}^nP_x=336\), then find n and x.

A five-digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is:

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is:

How many arrangements can be formed out of the letters of the word EXAMINATION so that vowels always occupy odd places?