A junior executive looking at his business attire in his closet notes that he has five suits,six shirts,and three pairs of shoes.He is going on a business trip and needs to take two of each.How many different combinations of outfits could he take?
A)680
B)320
C)450
D)224

Question

Quizplus · Accepted Answer

To find the total number of possible combinations of outfits, we need to multiply the number of options for each item of clothing:

Number of suits = 5
Number of shirts = 6
Number of pairs of shoes = 3

To find the number of combinations of 2 suits, we use the formula for combinations:
5 choose 2 = 5! / (2! * (5-2)!) = 10

Similarly, to find the number of combinations of 2 shirts and 2 pairs of shoes, we get:

6 choose 2 = 6! / (2! * (6-2)!) = 15
3 choose 2 = 3! / (2! * (3-2)!) = 3

To find the total number of combinations, we multiply these numbers together:
10 * 15 * 3 = 450

Therefore, the best choice is C.

A Junior Executive Looking at His Business Attire in His