Question

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible

Answer 1

Answer:

80

Step-by-step explanation:

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 sr officers and 1 jr officer, how many different committees are possible?

8

24

58

80*

210

I initially got this one wrong, but after I saw the answer which is 80, I was able to solve it. But im not sure if this is the proper way of solving it, or if someone can suggest a more efficient way of solving it?

This is what I did, which was wrong:

Sr Officers + Jr Officers

(6!/3! 3! = 20) + (4!/3! = 4) = 24

It seems like the correct answer is:

Sr Officers X Jr Officers

(6!/3! 3! = 20) x (4!/3! = 4) = 80

If this is the most efficient way of solving, when do you know when to add them as opposed to multiplying them in this case?