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}=(3!)/(2!1!)=(3\cdot 2!)/(2!) = 3`

Number of ways of choosing 1 skirt =
`_(1)^(4)\textrm{C}=(4!)/(3!1!)=(4\cdot 3!)/(3!) = 4`

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