Question

There are four letters available to make up a car number plate, W, X, Y and Z. The number plate must have only three letters, but they can be placed in any order. How many different number plates can you make?​

Answer 1

Using permutation formula P(n, k) = n! / (n-k)!, where n is 4 and k is 3, we find that there are 24 different number plates that can be made from the letters W, X, Y, and Z with only three letters on each plate.

Step-by-step explanation:

To determine how many different number plates can be made using four available letters (W, X, Y, Z) with the restriction that only three letters can be used for each plate, one can calculate the permutations of the four letters taken three at a time. The formula used for permutations where order matters is P(n, k) = n! / (n-k)!, where n is the total number of items to pick from, and k is the number of items to pick.

In this case, n = 4 (since there are four letters), and k = 3 (since we are making number plates with three letters). Therefore, the number of different permutations is P(4, 3) = 4! / (4-3)! = (4 × 3 × 2 × 1) / (1) = 24. Thus, you can make 24 different number plates.