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).

In the row, we will have 3 positions.

first position

second position

third position.

Let's use the notation:

(1, 2, 3)

to describe the first, second and third positions respectively.

If we can put 3 elements there (a teddy bear (T), a kitten (K), and an elephant (E))

The sample space will be all the possible elements of the form (1, 2, 3)

For example, the element where the teddy bear is in the first position, the kitten is in the second position, and the elephant is in the third position can be written as:

(T, K, E)

And because a single toy can not be in two different positions, the elements like (T, T, T) are not allowed, so the sample space will be the set of the permutations of:

(T, K, E)

(So we just reorder these elements in all the possible different ways)

That set is:

(T, K, E); (T, E, K); (E, T, K); (E, K, T); (K, T, E), (K, E, T)

Then the sample space will be:

S = {(T, K, E); (T, E, K); (E, T, K); (E, K, T); (K, T, E), (K, E, T)}

A space defined by these 6 elements.

step-by-step explanation:

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