Peg has 4 long-sleeve shirts, 5 short-sleeve shirts, and 6 pairs of pants. (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)

So the number of total combinations is 24+30=54.

Step-by-step explanation:

We know that Peg has 4 long-sleeve shirts, 5 short-sleeve shirts, and 6 pairs of pants. We assume that she is going to wear a shirt and a pair of pants.

First, we calculate the number of combinations for a pants and long-sleeve shirts. She have 6 pairs of pants and 4 long-sleeve shirts.

We get: 6 · 4 = 24

Now, we calculate the number of combinations for a pants and short-sleeve shirts. She have 6 pairs of pants and 5 short-sleeve shirts.

We get: 6 · 5 = 30

So the number of total combinations is 24+30=54.