Question

How many ways are there to pick a subset of 3 different letters from the 26-letter alphabet?

1) Combination; C₃₂ = 1771
2) Permutation; P₃₂ = 10626
3) Permutation; P₃₂ = 15600
4) Combination; C₃₂ = 2600

Answer 1

1) Combination; C₃₂ = 1771. The number of ways to pick a subset of 3 different letters from the 26-letter alphabet is 2600.

Step-by-step explanation:

The number of ways to pick a subset of 3 different letters from the 26-letter alphabet can be found using combinations.

The formula for combinations is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items being chosen.

For this question, n=26 and r=3. Plugging these values into the formula, we get:

C(26, 3) = 26! / 3!(26-3)! = (26 * 25 * 24) / (3 * 2 * 1) = 2600

So, the correct answer is:

1. Combination; C₃₂ = 2600