Question

John has 6 pairs of pants and 3 shirts. How many possible outfits consisting of one shirt and

one pair of pants can he select?

Answer 1

John can create 18 possible outfits from his 6 pairs of pants and 3 shirts by using the multiplication principle of counting, which gives a result of 6 times 3.

Step-by-step explanation:

To determine the number of possible outfits John can select with his 6 pairs of pants and 3 shirts, we use the basic principle of counting. Each pair of pants can be matched with any of the shirts, so for each pair of pants, there are 3 choices of shirts. This scenario represents a fundamental problem in combinatorics, which is the study of counting.

The multiplication principle of counting states that if there are m ways to do one thing, and n ways to do another, then there are m times n ways to do both. Here, John has 6 ways (pairs of pants) and 3 ways (shirts) to make a choice, resulting in a total of 6 × 3 = 18 possible outfits.

The calculation is straightforward:

Number of possible outfits = Number of pants × Number of shirts

Number of possible outfits = 6 (pairs of pants) × 3 (shirts) = 18 possible outfits.

Answer 2

4*5*7=140 ways

Step-by-step explanation:

First he has to decide on a pair of pants and he has 4 different choices.

For each of those choices he has a choice of 7 different shirts, so that gives him 4 times 7 = 28 different pant/shirt combinations. (I hope none of the pants are striped and none of the shirts have polka-dots).

For each those 28 possibilities, he has 5 different ties he could select, so altogether he has 28 times 5 = 140 different outfits, and some of them may be acceptable to wear in public.

It is simply , 4*5*7=140 ways.