Question

1. the letters of the word house are to be rearranged.

6a how many different arrangements are possible?
arrangements = 120
5 nailed it!
6b what is the probability that the letter e will be the first letter?
probability = enter your next step here

Explanation:

Step1: Determine favorable outcomes

If E is first, the remaining 5 letters (H, O, U, S, E? Wait, no, HOUSE has 6 letters: H, O, U, S, E? Wait, H-O-U-S-E: that's 5 letters? Wait, no, H-O-U-S-E: H, O, U, S, E – 5 letters? Wait, the first part (6a) says arrangements = 120, which is 5! = 120. So HOUSE has 5 distinct letters? Wait, H, O, U, S, E – 5 letters, all distinct. So if E is first, then we arrange the remaining 4 letters: 4! = 24.

Step2: Total possible arrangements

From 6a, total arrangements are 120 (which is 5! = 120, since 5 distinct letters).

Step3: Calculate probability

Probability is favorable outcomes / total outcomes = 24 / 120 = 1/5. Alternatively, since there are 5 distinct letters, the probability that E is first is 1/5 (since each letter has an equal chance to be first, and there are 5 letters).

Answer:

$\frac{1}{5}$ (or 0.2)