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nC3 = nC10 then n = ____?
  1. 10
  2. 13
  3. 30
  4. None of these
Explanation

Let's solve the problem:
Given (n3)=(n10), find n.

Step 1: Use the symmetry property of binomial coefficients

We know that (nk)=(nn−k).
So, (n3)=(nn−3).

Step 2: Set equal to the given term

Given (n3)=(n10),
so (nn−3)=(n10).

This implies:

n−3=10orn−3=n−10(but the latter is invalid)

So,

n−3=10  ⟹  n=13

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