Help Answer the following questions using the pigeonhole principle. Show your wo

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Answer the following questions using the pigeonhole principle. Show your work in each case. How many students should there be in a class so that at least 3 of them have the same last - name initial? How many should be there so that least 2 of them have the same first - name and last - name initials? How many integers you must select from the set {1, 2, 3,...,2n), to make sure that at least one of them is even? How many people, should be there in a group so that at least 5 have the same birthday?

Explanation / Answer

1) Let the no of students be N

so ceil of N/26 = 3 as last name initial can be any alphabet

so N = 78.

2) ceil of N/26*26 = 2

so N = 1352

3) ceil of N/n+1 = 1

so N = n+1

4) ceil of N/365 = 5

so N = 1825

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