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.

Step-by-step explanation:

She can choose any combination of 3 of the 10 shirts

and any combination of 2 of the 5 pairs of pants.

C(10,3) C(5,2)

= [10! / (7! 3!)] [5! / (3! 2!]

= [10 * 9 * 8 / (3 * 2 * 1)] [5 * 4 / (2 * 1)]

= (5 * 3 * 8) (5 * 2)

= 120 * 10

= 1200 possible combinations of clothes to pack.  

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step-by-step explanation:

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step-by-step explanation: