Question

There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

Answer 1

The number of shoes required to drawn out, to ensure that at least one pair of black shoes are taken out is 4*2+2=10

Answer 2

Given:

7 pairs of black shoes

5 pairs of white shoes

To Find:

Number of draws needed to draw one pair of black shoes

Explanation:

A pair of shoes has a left side and a right side. So drawing 2 left sides of the shoes does not constitute to a pair fo shoes. A left side and a right side is needed.

Solution:

Find the number of white shoes:

Number of pairs = 5

Number of shoes = 5 x 2

Number of shoes = 10

Find the number of black shoes:

Number of pairs = 7

Number of shoes = 7 x 2

Number of shoes = 14

Consider the worst case scenarios:

All the white shoes were drawn before any of the black shoes were drawn.

Number of draws = 10

Now we are left with all the black shoes. All the left sides were drawn.

Number of draws = 7

Now whatever remains are all the right side of the black shoes. So any one draw from this stack will give us a pair.

Number of draws = 1

Find the total number of draws needed:

Total number of draws needed = 10 + 7 + 1

Total number of draws needed = 18

Answer: 18 draws are needed to ensure that there are at least one pair of black shoes.