Question

A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be drawn from it such that there will be no complete pair is?

A. 80
B. 160
C. 200
D. None of the foregoing numbers

Answer 1

The number of ways to select 4 shoes from 5 pairs with no complete pair is calculated by selecting one shoe from 4 pairs and then multiplying by the number of ways to choose the pair to exclude, resulting in 80 ways. So the correct answer is option A.

Step-by-step explanation:

The question relates to the concept of combinations in probability and combinatorics. To find the number of ways to select 4 shoes from 5 pairs such that no complete pair is selected, we choose one shoe from each of the first 4 pairs and then the last shoe from the remaining fifth pair. The calculation works as follows:

• Select one shoe from the first pair: 2 ways
• Select one shoe from the second pair: 2 ways
• Select one shoe from the third pair: 2 ways
• Select one shoe from the fourth pair: 2 ways
• Select one shoe from the fifth pair: 2 ways

However, since we only need to choose 4 shoes and not 5, we need to choose which pair we're not taking a shoe from. There are 5 pairs, so there are 5 ways to choose the pair to exclude.

The total number of ways is therefore:

2 ways/pair * 2 ways/pair * 2 ways/pair * 2 ways/pair * 5 pairs to exclude = 80 ways.

So, the correct answer is A. 80.