Permutations or combination not sure

[Ruby_Salamone]

Your club plans to select a nominating committee from its 24 members. By the bylaws, the 8 officers cannot serve on the nominating committee. How many ways can you select this committee if it must have 8 people on it?

 

[JeffM]

How many members can you select from?

What is the formula for selecting k from n?

 

[Dr.Peterson]

Permutations are ways of arranging items in some order. Does order matter here?

Combinations are ways of choosing some from a set, without distinguishing order.

 

[Ruby_Salamone]

Order matters in many situations.

1. Your club will elect a slate of 8 officers from among 24 men and women. How many ways can you select the slate?

answer: 29654190720

2. Your club plans to select a nominating committee from its 24 members. By the bylaws, the 8 officers cannot serve on the nominating committee. How many ways can you select this committee if it must have 8 people on it?
(this was the second half of the question that i did not understand

 

[Dr.Peterson]

1. It's important to show your work, if only to make it easier for others to see whether you are doing the right thing. Mere numbers are too anonymous. After calculating, I see that you chose to use permutations; here the problem could have been clearer, as it doesn't explicitly say the 8 officers have distinct offices (as you are assuming), so you are going by cultural expectations rather than what is actually stated. It is conceivable that the "slate of 8 officers" could just be 8 equal leaders, in which case combinations would be appropriate. I suppose you are probably right, but I wish the problem had been explicit, as these usually are.

2. The committee definitely consists of 8 undistinguished positions, so combinations are appropriate. As I read it, the 8 officers have been elected, leaving 16 non-officers, from whom 8 on the committee are to be chosen.