explain pigeonhole principle. using this principle show that in a group of 36 people we can always find 6 people who were born on the same day of week

Question

anonymous · Answer

The pidgeonhole principle: if we put n things in k containers, and if m is the least integer which is greater than or equal to n/k, then there is a container which contains m or more things.

Let the people be the things (n=36) and let the days of the week be the containers (k=7). Because n/k is 5 + 1/7, m=6. By the pidgeon hole principle, there is a container which contains m or more things, i.e. there is a day of the week on which at least 6 people were born.

kc_kennylau · Answer

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