Question

Tim must choose 4 graphic novels out of a collection of 13 to take on vacation.

Answer 1

Answer:

C. 17,160

Step-by-step explanation:

Given : Tim need to choose 4 graphic novels out of a collection of 13 .

To Find : No. of ways he can select the graphic novels.

Solution :

Since we are supposed to find the number of ways so we have to use combination over here

Formula :

$_{n}C_{r}=\frac{n!}{(r)!*(n-r)!}$

Since n = 13 (given)

         r = 4(given )

put the values in the given formula :

$_{n}C_{r}=\frac{13!}{(4)!*(13-4)!}$

$_{n}C_{r}=\frac{13!}{(4)!(9)!}$

$_{n}C_{r}=\frac{13*12*11*10*9!}{(4)!*(9)!}$

$_{n}C_{r}=\frac{13*12*11*10}{(4)!}$

$_{n}C_{r}=\frac{13*12*11*10}{(4*3*2*1}$

$_{n}C_{r}=715$

Thus , He can select graphic novels in 715 number of ways

Hence Option C is correct.

Answer 2

Answer: 715 ( C )

Explanation:

C (13,4) = (13!)/(4!*9!)

So it can be done on the calculator by 13C4  

13! = 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

4! = 4 x 3 x 2 x 1

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / ( 4 x 3 x 2 x 1 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 )

6,227,020,800 / 8,709,120

=715

So the correct answer is C, 715