If `.^(n)C_(r-1)=36,.^(n)C_(r)=84 and .^(n)C_(r+1)=126`, find find r.

Explanation

To solve the problem, we are given the following equations based on combinations:

1. \( \binom{n}{r-1} = 36 \)
2. \( \binom{n}{r} = 84 \)
3. \( \binom{n}{r+1} = 126 \)

We need to find the value of \( r \).

...