Question

A club consists of 7 women and 5 men and needs to select an executive council consisting of President, Vice President, and Secretary. What is the probability that a chosen executive council will have a President and Vice President of different genders?

a) 7/11
b) 35/66
c) 10/66
d) 7/66

Answer 1

The probability of selecting a President and Vice President of different genders in the club is 35/66.

Step-by-step explanation:

To calculate the probability that the chosen executive council will have a President and Vice President of different genders, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.

There are 7 women and 5 men in the club. We can choose the President and Vice President in the following ways:

• Choose a woman as President and a man as Vice President: 7 choices for President and 5 choices for Vice President.
• Choose a man as President and a woman as Vice President: 5 choices for President and 7 choices for Vice President.

Therefore, the total number of ways to choose a President and Vice President of different genders is 7 * 5 + 5 * 7 = 70.

The total number of possible outcomes is the number of ways to choose any 2 people from the club, which is 12 choose 2 = (12 * 11) / (2 * 1) = 66.

So, the probability is 70/66 = 35/33.

The correct answer is option b) 35/66.