Question

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

• A. \( \frac{1}{720} \)
• B. \( \frac{1}{80} \)
• C. \( \frac{1}{10} \)
• D. \( \frac{1}{9} \)
• E. \( \frac{1}{5} \)

Hint:

For problems involving probability, calculate the total outcomes and favorable outcomes, then divide.

Answer 1

The Correct Option is D

Step 1: Total number of possible outcomes.
The total number of ways to select the president, secretary, and treasurer is: \[ 10 \times 9 \times 8 = 720 \] Step 2: Favorable outcomes where Harry is secretary or treasurer.
- If Harry is the secretary, the president can be selected from 9 members and the treasurer from 8 remaining members: \[ 9 \times 8 = 72 \] - If Harry is the treasurer, the president can be selected from 9 members and the secretary from 8 remaining members: \[ 9 \times 8 = 72 \] Thus, the total favorable outcomes are: \[ 72 + 72 = 144 \] Step 3: Probability calculation.
The probability is: \[ \frac{144}{720} = \frac{1}{5} \] \[ \boxed{\frac{1}{9}} \]