Question

If n+1 integers are chosen from the set

Answer 1

Answer:

Pigeonhole Principle

Step-by-step explanation:

From series {1,2......2n} ; we need to select 'n + 1' integers.

Even integers series from above series = {2,4,6..........2(n-1), 2n}

Odd integers series from above series = {1,3,5........2(n-2), 2n-1}

So, we can choose only n odd integers from the series. Hence, if we choose n+1 integers, atleast one of them have to be even integer.

• Eg : n = 5, Series = (1,2,3,4,5,6,7,8,9,10}, Odd series = {1,3,5,7,9}, Even series = {2,4,6,8,10}. If we choose 5 +1 ie 6 integers, there must be one even integer, as there are only 5 total odd integers in series.