# Math final review: counting problems

#### nickar1172

##### New member
Can somebody please give me a heads up on if I solved these two problems correctly, I appreciate it, thank you!

d) In setting up a new department, a corporation executive must select a manager from among 4 applicant, 3 clerks from among 9 applicants, and 2 secretaries from among 7 applicants. In how many ways can these positions be staffed

I got 1C4 x 9C3 x 7C2 = 7056

e) A customer can purchase a sports car in either the convertible or hardtop model, in any of 6 colors, and with any of three accessory packages. How many options are open to the purchaser?

I got 2! x 3! x 6! = 8640

#### Jameson

Staff member
Re: Math FINAL review

Can somebody please give me a heads up on if I solved these two problems correctly, I appreciate it, thank you!

d) In setting up a new department, a corporation executive must select a manager from among 4 applicant, 3 clerks from among 9 applicants, and 2 secretaries from among 7 applicants. In how many ways can these positions be staffed

I got 1C4 x 9C3 x 7C2 = 7056

e) A customer can purchase a sports car in either the convertible or hardtop model, in any of 6 colors, and with any of three accessory packages. How many options are open to the purchaser?

I got 2! x 3! x 6! = 8640
Hi nickar1172,

I agree with your first answer, except for one typo I think you made. Instead of "1C4" it should be "4C1". The result seems correct though.

As for the second question, I don't see why the factorials are needed in each space. The car can be "any of 6 colors", not all 6 colors. So there are 6 options for colors, not 6! options as I see it. Same thing for the other two qualities.

What do you get now?

#### nickar1172

##### New member
Re: Math FINAL review

Hi nickar1172,

I agree with your first answer, except for one typo I think you made. Instead of "1C4" it should be "4C1". The result seems correct though.

As for the second question, I don't see why the factorials are needed in each space. The car can be "any of 6 colors", not all 6 colors. So there are 6 options for colors, not 6! options as I see it. Same thing for the other two qualities.

What do you get now?
I'm lost on e) I got it wrong on the quiz and tried to redo it but I guess that answer is still wrong would you mind posting how to solve / get the solution please? Also what type of question it is

#### Jameson

You were close, but you need to drop the factorials. The answer is $2 \times 3 \times 6$ as there are 2 options for the first choice, 3 for the second and 6 for the third.