Math final review: counting problems

[nickar1172]

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]

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]

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]

Re: Math FINAL review

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

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.

 

[CellCoree]

I cannot give a definitive answer on whether or not your solutions are correct without seeing your work and knowing the specific problem set. However, your solutions appear to be using the correct formulas for counting problems. In problem d), you correctly used the combination formula (nCr) to determine the number of ways to select managers, clerks, and secretaries from their respective applicant pools. In problem e), you correctly used the factorial (n!) formula to determine the number of options for the sports car. However, it is always a good idea to double check your work and make sure you are using the correct formulas for each problem. Good luck on your final review!