Question

compute the following: $_8c_3 _5c_2
a. 6720
b. 5.6
c. 3360
d. 560
please select the best answer from the choices provided

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$.

Step2: Calculate $_{8}C_{3}$

$_{8}C_{3}=\frac{8!}{3!(8 - 3)!}=\frac{8!}{3!5!}=\frac{8\times7\times6\times5!}{3\times2\times1\times5!}=56$.

Step3: Calculate $_{5}C_{2}$

$_{5}C_{2}=\frac{5!}{2!(5 - 2)!}=\frac{5!}{2!3!}=\frac{5\times4\times3!}{2\times1\times3!}=10$.

Step4: Multiply the two combinations

$_{8}C_{3}\times_{5}C_{2}=56\times10 = 560$.

Answer:

D. 560