A cricket squad has 14 players. In how many ways can a team of 11 players be…

The number of ways to choose r items from a set of n items when the order of selection does not matter is given by the combination formula, nCr = n! / (r! × (n − r)!). This counts every distinct group of r items exactly once, regardless of the sequence in which its members are picked.

1. Here n = 14 (players in the squad) and r = 11 (players needed in the playing team), so the count is 14C11 = 14! / (11! × 3!).

2. Since 14! / 11! cancels down to the product of the three largest factors, 14C11 = (14 × 13 × 12) / (3 × 2 × 1).

3. Multiply the numerator: 14 × 13 = 182, and 182 × 12 = 2184.

4. Multiply the denominator: 3 × 2 × 1 = 6.

5. Divide: 2184 ÷ 6 = 364.

Cross-check: Choosing which 11 of the 14 players play is the same as choosing which 3 players sit out, so 14C11 must equal 14C3. Computing 14C3 directly gives (14 × 13 × 12) / (3 × 2 × 1) = 364 as well, confirming the result.

So a team of 11 players can be selected from the squad of 14 in 364 ways.