Question

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

(6a) how many different arrangements are possible?
arrangements = 120
(6b) what is the probability that the letter e will be the first letter?
probability = \\(\frac{1}{5}\\)
(6c) what is the probability that the letters are arranged in alphabetical order?
probability = enter your next step here

Explanation:

Step1: Determine Total Arrangements

From part (a), the total number of arrangements of the 5 distinct letters in "HOUSE" (H, O, U, S, E) is \( 5! = 120 \).

Step2: Determine Favorable Outcomes

There is only 1 way to arrange the letters in alphabetical order (E, H, O, S, U).

Step3: Calculate Probability

Probability is the number of favorable outcomes divided by the total number of outcomes. So, \( \text{Probability} = \frac{1}{120} \).

Answer:

\( \frac{1}{120} \)