Permutation and Combination

Permutation:

1: The action of changing the arrangement, especially the linear order, of a set of items.

2: All possible arrangements of a collection of things, where the order is important.

Example: You want to visit the homes of three friends Alex ("a"), Betty ("b") and Chandra ("c"), but haven't decided in what order. What choices do you have?

Answer: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a}

Combination:

A collection of things, in which the order does not matter.

Example: If you are making a sandwich, how many different combinations of 2 ingredients could you make with cheese, mayo and turkey?

Answer: {cheese, mayo}, {cheese, turkey} or {mayo, turkey}

 

1

From 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?

2

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

3

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

4

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?