You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each? Explain your answer. a. 4.5+3 = 23 b. 4…

Question

asked Jun 9, 2020 56.9k views

2 Answers

Henry Henrinson · Answer 1 · 2020-06-16T15:07:08+0000

Answer:

C.
$4\cdot 5\cdot 3 = 60$

Explanation:

Given:

Number of sweaters are,
S=4

Number of pair of pants are,
P=5

Number of pairs of shoes are,
H=3

Now, as per question, we have to choose one from each type.

Now, number of ways of choosing one sweater from 4 sweaters is
$n(S)= 4\ ways$ .

Number of ways of choosing one pair of pants from 5 pair of pants is
$n(P)= 5\ ways$ .

Number of ways of choosing one pair of shoes from 3 pairs of shoes is
$n(H)= 3\ ways$ .

Therefore, choosing one from each type is the intersection of all. So,

$n(S\cap P\cap H)=n(S)\cdot n(P)\cdot n(H)\\n(S\cap P\cap H)=4\cdot 5\cdot 3\\n(S\cap P\cap H)=60$

Therefore, 60 different combinations can be made wearing one of each type.