Question

19. Fifteen students volunteer for a committee. How many different eight-person committees can be chosen?

6435 committees
40,320 committees
5040 committees
259,459,200 committees

20. The rate of discount R, can be determined using the formula R = 1 – P-D over P, where P is the regular price of an item and D is the discount, or amount saved off the regular price. Find the rate of discount on a sweater with a regular price of $28.99 that is on sale for $10.99.

37.9%
$10.99
$18
62.1%

Answer 1

We have to choose 8 out of 15.
Assuming the order is not important (because there is nothing said about different jobs within the committee), you have to calculate the number of combinations of 8 out of 15. Notation: \[\left(\begin{matrix}15 \\ 8\end{matrix}\right)=\frac{ 15! }{ 8!(15-8)! }=\frac{ 15! }{ 8!7! }\]These numbers get very large, but let's give it a try:\[\frac{ 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 }{ 8*7*6*5*4*3*2*1* 7*6*5*4*3*2*1}\]Factors 1-8 are both in the nominator and the denominator, so they cancel out. This is what is left:\[\frac{ 15*14*13*12*11*10*9 }{ 7*6*5*4*3*2*1 }=\]Already a lot less to calculate. Because 15=5*3 and 14=2*7, these factors also go away:\[\frac{ 13*12*11*10*9 }{ 6*4*1 }=\frac{ 13*11*10*9 }{ 2 }=13*11*5*9=6435\]