Question

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. How many different outfits can John make?

Answer 1

Concept

The act or way of selecting items or numbers from a group of items is called as Combination.

Permutation is the way or act of arranging the items in a manner.

Given

John owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts

Find

How many number of different outfits can he make?

Solution

This is a question based on Permutations and Combinations

Now we have different possibilities or combinations of selecting what he would wear. That can be calculated by the following formula:

Number of combinations of selecting shirt = 5C1 = 5ways

Number of combinations of selecting a pant = 10C1 = 10 ways

Number of combinations of a pair of socks = 12C1=12 weeks

Number of combinations of selecting pair of shoes = 3C1 = 3 ways.

Hence the total number of possible combinations can be calculated as the product of the number of ways.

⇒ 5 × 12 × 10 × 3 = 1800 ways

Therefore John can make 1800 different kinds of outfits.

#SPJ2

Answer 2

$\qquad {\boxed{\bold\green{Answer=1800\:ways}}}$

Step-by-step explanation:

$\bf{Given}\begin{cases}\sf{Socks=12\:pair}\\\sf{Shoes=3\:pairs}\\\sf{Pants=5\:pairs}\\\sf {Shirts=\:5}\end{cases}$

Formula used:- Combination formula.

_____________________

$\sf \star \ Number\:of\:combination\:of\:selecting\:a\:pair\:of\:socks=12C_1 = 12\:ways.\\\\\sf \star \ Number\:of\:combination\:of\:selecting\:a\:pair\:of\:shoes=3C_1=3\:ways\\\\\sf \star \ Number\:of\:combination\:of\:selecting\:a\:pant=10C_1 =10\:ways.\\\\\sf \star \ Number\:of\:combination\:of\:selecting\:a\:shirt=5C_1=5\:ways. \\\\\rightarrow\sf Total\:ways\:that\:John\:can\:make\:outfits:-\\\\ \rightarrow\sf Total\:ways=12\times 3 \times 10 \times 5 \\\\\rightarrow\sf Total\:ways=1800\:ways. \\\\\\\therefore\bold{\underline{John\:can\:make\:total\:1800\:different\:outfits.}}$