Question

Vijay enjoys cycling every morning. As it is very cold outside, he usually takes his gloves when he goes out for cycling. He has 2 pairs of blue gloves, 8 red pairs and 15 purple pairs. One day, while he was about to take his gloves from the cupboard, the power goes off.

Vijay wants to wear purple gloves to match the colour of his shirt. Since he was searching in the dark, he knew that he would definitely get a pair of purple gloves if he took out all the 50 gloves from the cupboard. However, he wants to pick the least possible number of gloves and make sure it has a pair of purple gloves.

What is the minimum number of gloves he should take out from the cupboard in order to be sure to have at least one pair of purple gloves?

Answer 1

Step-by-step explanation:

So, it is given: There are totally about 50 gloves in the cupboard.

To Prove: The least number of gloves to make sure that it has at least one pair of purple gloves.

Solution: There are 15 pairs of purple gloves in his cupboard. That is, 30 individual purple gloves.

So, even if he picks 20 gloves, there is no assurity of getting a purple glove in it. Only if he pick 22 gloves, there is a chance that he gets at least one pair of purple gloves.

Hope this helps.