Question

L'shanda can choose between 3 sweaters and 4 skirts. if she selects 1 sweater and 1 skirt, how many possible outcomes are in the sample space answer

Answer 1

Nuber of outcomes = 3 * 4  = 12 Answer

Answer 2

We have been given that L'shanda can choose between 3 sweaters and 4 skirts.

We need to figure out the number of ways in which L'shanda can pick 1 sweater and 1 skirt out of the available items.

We need to use combinations here. First of all, we will figure out the number of ways of choosing 1 sweater out of 3 available sweaters. And then we will determine the number of ways of choosing 1 skirt out of 4 available skirts.

Number of ways of choosing 1 sweater = $_{1}^{3}\textrm{C}=\frac{3!}{2!1!}=\frac{3\cdot 2!}{2!} = 3$

Number of ways of choosing 1 skirt = $_{1}^{4}\textrm{C}=\frac{4!}{3!1!}=\frac{4\cdot 3!}{3!} = 4$

Therefore, total number of ways to select 1 sweater and 1 skirt are $3\cdot 4 = 12$