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

A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of c…

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come t…

A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee…

From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to inc…

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only th…

In how many ways can six different rings be worn on four fingers of one hand?

In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?