In how many different ways can the letters of the word OPERATE be arranged ?

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetiti…

How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?

In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

A two member committee comprising of one male and one female member is to be constitute out of five males and three fema…

How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?