Respuesta :
Step-by-step explanation:
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.
For example If John has 2 pants and 3 shirts
he make an combination of 1 pant with 3 shirts
and another pant with 3 shirts
so total of 6 combination he can make (2*3)= 6
To find the number of combination we multiply all the shirt, pants, socks, and shoes he have
12pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts.
12 * 3 * 5 * 5 = 900
So 900 different combination John can make
Combination helps us to find a number of ways. The number of ways John can wear an outfit is 900.
What is the Combination?
A combination helps us to find the number of ways something can be selected from a set. It is given by the formula,
[tex]^nC_r = \dfrac{n!}{r!(n-r) ! }[/tex]
where n is the total number of choices in the set, r is the number of choices we want.
Given to us
Number of pairs of socks = 12
Number of pairs of shoes = 3
Number of pants = 5
Number of shirts = 5
The number of ways John can wear an outfit can be found out using the combination of shirt, socks, pants, and shoes. Therefore,
Number of ways John can wear an outfit
= Number of ways John wears shocks x Number of ways John wears shoes x Number of ways John wears pants x Number of ways John wears a shirt
Number of ways John can wear an outfit
[tex]= ^{12}C_1 \times ^{3}C_1 \times ^{5}C_1 \times ^{5}C_1 \\[/tex]
= 900
Hence, the number of ways John can wear an outfit is 900.
Learn more about Permutation and Combination:
https://brainly.com/question/14767366
