Question

Rajat draws a \(10 \times 10\) grid with squares numbered 1 to 100. He places two identical stones on any two separate squares. How many distinct ways are possible?

• A. 2475
• B. 4950
• C. 9900
• D. 1000

Hint:

For selecting 2 identical items on different positions, use combination formula: \(\binom{n}{2}\).

Answer 1

The Correct Option is B

We are choosing 2 distinct squares out of 100 to place identical stones. Number of ways to choose 2 squares out of 100: \[ \binom{100}{2} = \frac{100 \times 99}{2} = \boxed{4950} \] Because the stones are identical, the arrangement (square A, square B) is the same as (square B, square A), so we divide by 2 only once.