Question

2m Where m is any positive integer​

Answer 1

Answer:

m is not the integer it is a variable

Answer 2

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m is a positive integer and set S={1,2,3,⋯,2m+1}.

⇒ The set S has m even numbers and m+1 odd numbers.

We want to choose 3 distinct numbers from S such that their sum is even.

This can be done either by selecting 3 even numbers or by selecting 2 odd and 1 even numbers.

We can choose 3 even numbers out of m numbers in C(m,3) ways.

We can choose 2 odd and 1 even numbers out of m+1 numbers in C(m+1,2)C(m,1) ways.