Question

Alan is arranging 3 different stuffed toys in a row on a shelf. create a sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e).

Answer 1

The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

How to create the sample space?

The given parameters are

Stuffed toys, n = 3

Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).

The number of arrangement is calculated as;

Ways = nPr

Substitute the known values in the above equation

Ways = 3Pr

Apply the permutation formula

Ways = 3!/0!

0! =1

So, we have

Ways = 3!/1

This gives

Ways = 3!

Expand

Ways = 3 * 2 * 1

Evaluate

Ways = 6

This means that the sample size is 6

Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt

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