Question

Faith and Shawna are shopping for shirts. The available styles are short sleeve (s), tank top (t), and long sleeve (L). they make a list to show all possible outcomes if each girl buys a new shirt. is the list complete? Explain. (s,t), (s,s), (s,L), (T,T), (T,S), (T,L), (L,L), (L,T), (L,S)

Answer 1

The number of ways of selection of 3 items taking 2 at a time in addition to the possible ways in which each girl selects the same style is 9 different ways. Since the list contains 9 different ways in which each of them can select a style, the list is complete.

Explanation:

Here we have the number of ways the available styles can be arranged between each girl is given by the number of permutation of 3 items, taking two at a time plus the number of possible selections where both of them select the same style as follows

We note that the formula for permutation is

`_n`P
`_r` =
`(n!)/((n-r)!)`

Therefore ₃P₂ =
`(3!)/((3-2)!)` = 6 different ways

The number of possible selections where both of them select the same style is given by

(T, T), (s, s), (L, L) = 3 different ways

Total number of ways = 6 + 3 = 9 ways

Number of different ways available in the list = 9 ways

Therefore the list is complete