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

If $$5{ \times ^{\text{n}}}{{\text{P}}_3} = 4{ \times ^{\left( {{\text{n}} + 1} \right)}}{{\text{P}}_{3,}}$$   …

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alph…

The number of ways of arranging n students in a row such that no two boys sit together and no two girls sit together is …

There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that the…

12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs num…

In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person i…

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