Question

a committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 8 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

Answer:

42042 number of ways can the committee be formed.

Step-by-step explanation:

Given: There are 8 Faculty member and 15 students eligible to serve on the committee.

Need to form a committee of 4 faculty and 5 students.

Now, finding the number ways that committee to be formed.

lets use the combination formula to find combination of faculty and students.

$_{r}^{n}\textrm{C}= \frac{n!}{r!(n-r)!}$

Subtituting the value in the formula

⇒ $_{4}^{8}\textrm{C}\times _{5}^{15}\textrm{C}= \frac{8!}{4!(8-4)!} \times \frac{15!}{5!(15-5)!}$

⇒$_{4}^{8}\textrm{C}\times _{5}^{15}\textrm{C}= \frac{8\times 7\times 6\times 5\times 4!}{4!(4)!} \times \frac{15\times 14\times 13\times 12\times 11\times 10!}{5!(10)!}$

⇒$_{4}^{8}\textrm{C}\times _{5}^{15}\textrm{C}= \frac{8\times 7\times 6}{4\times 3\times 2\times 1} \times \frac{15\times 14\times 13\times 12\times 11}{5\times 4\times 3\times 2\times 1}$

⇒ $_{4}^{8}\textrm{C}\times _{5}^{15}\textrm{C}= 14\times 3003$

⇒$_{4}^{8}\textrm{C}\times _{5}^{15}\textrm{C}= 42042$

∴ 42042 number of ways can the committee be formed.