compute the following: $_8c_3 _5c_2\na. 6720\nb. 5.6\nc. 3360\nd. 560\nplease select the best answer from…
compute the following: $_8c_3 _5c_2\na. 6720\nb. 5.6\nc. 3360\nd. 560\nplease select the best answer from the choices provided
Answer
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