In how many different way can the letters of the word  ‘JUDGE’ be arranged so that the vowels always come together ?

In how many different way can the letters of the word  ‘AUCTION’ be arranged so that the vowels always come together ?

In how many different way can the letters of the word  ‘BANKING’ be arranged so that the vowels always come together ?

In how many different way can the letters of the word  ‘CORPORATION’ be arranged so that the vowels always come together ?

In how many different way can the letters of the word  ‘DETAIL’ be arranged so that the vowels always come together ?

In how many way can a group  of 5 men  and 2 women be made out of a total of 7 men and 3 women ?

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

Form a group of 7 men and 6 women , five persons are to be selected to form a committee so that at least 3 men are there on    the committee . In how many  ways can it be done ?

In a group of 6 boys and 4 girls, four children are  to be selected. in   how many different ways can they be selected such that at     least one boy should be there ?

A box contains 2 white balls , 3 black balls and 4 red balls . In how many ways can 3 balls be drawn from the box , if at least one    black ball is to be include in the draw ?