Question

Which of the following is an example of a combination

Answer 1

B and D are clearly permutation. A and B are selections but arrangement should be done for A where as C only requires selection so C is the combination.

Answer 2

The example which describes combination is:

• Selecting 5 CD's to take with you on a trip from a collection of 30 CD's.

Explanation:

Combination--

It is a method of choosing or selecting some items from a group of items.

The formula for choosing r items out of a total of n items is given by the formula:

`n_C_r=(n!)/(r!* (n-r)!)`

Also, if we are selecting as well as arranging some items from a group of items then that method is known as a method of permutation.

A)

Selecting the best cake and runner up best cake from a cake decorating competition.

In this case we are choosing as well as arranging the best and runner up cake according to their ranks.

Hence, it will be a process of permutation and not combination.

B)

The number of ways 6 people can arrive at a party if no one arrive at the same time.

Again it is a problem of permutation because we have to find the number of ways the people can arrive i.e. arranging people in different orders they may arrive.

C)

Selecting 5 CD's to take with you on a trip from a collection of 30 CD's.

This is a method of combination.

Since we have to select some items from a set of items.

D)

The number of ways triplets can be born.

This is again a process of permutation.

Since there are different order they may come.