Question

Suppose we want to choose letters, without replacement, from the letters A, B, C, D, and E. How many ways can this be done if the order of the choices is taken into consideration

Answer 1

There are 120 different ways to choose and order the letters A, B, C, D, and E without replacement. This is calculated as the factorial of the number of letters (5!), which equates to 5 × 4 × 3 × 2 × 1.

Step-by-step explanation:

When choosing letters from the set {A, B, C, D, E} without replacement and considering the order of choices, you are essentially looking at the number of permutations of the set. Since there are 5 letters, the number of ways to arrange these 5 letters is calculated by the factorial of the number of items, which is denoted as 5! (5 factorial).

The calculation for 5! is:

1. 5 × 4 × 3 × 2 × 1 = 120

Therefore, there are 120 different ways to arrange the set of 5 letters considering the order in which they are chosen.