A committee is to be chosen from a group of 11 women and 14 men. How many ways can they select a president, treasurer, and secretary, if the treasurer and secretary must be males? No person can serve in more than one position. Show work to support your answer
number of ways to pick P, T, and S
= 14 x 13 x 23
= 4186
To find the number of ways the committee can select a president, treasurer, and secretary, we need to first determine the number of options for each position.
1. Selecting the president: Since there are no restrictions on the gender of the president, any of the 11 women or 14 men can be chosen. So, there are a total of 11 + 14 = 25 options.
2. Selecting the treasurer: Since the treasurer must be a male, we can only choose from the 14 men available.
3. Selecting the secretary: Similar to the treasurer, the secretary must also be a male. Therefore, we can choose from the remaining 13 men after selecting the treasurer.
To find the total number of ways to select a president, treasurer, and secretary, we multiply the number of options for each position:
Total options = Number of options for president × Number of options for treasurer × Number of options for secretary
= 25 × 14 × 13
Calculating the total gives us: Total options = 4550
Therefore, there are 4550 different ways the committee can select a president, treasurer, and secretary.