Question

The grade appeals process at a university requires that a jury be structured by selecting six individuals randomly from a proof of seven students and six faculty. A) what is the probability of selecting a jury of all faculty? B) what is the probability of selecting a jury of three students and three faculty ?

Answer 1

Out of $7$ students and $6$ faculty , a jury of six individuals can be select in $^{13}C_6$ ways.

Therefore sample space $S$ contains $^ {13}C_6$ number of elements.

(A) There are $6$ faculty. So out $6$ faculty a jury of 6 persons can be select in $^6C_6$ ways.

Let $A$ be en event such that selecting a jury of all faculty.

Then $P(A)=\frac{n(A)}{n(S)}=\frac{^6C_6}{^{13}C_6}=\frac{1}{1716}$

(B) Let $B$ be an event such that selecting a jury of $3$ students and $3$ faculty.

Now a jury of $3$ students and $3$ faculty out of $7$ students and $6$ faculty can be select in $(^7C_3×{ ^6C_3})$ ways.

Then $P(B)=\frac{n(B)}{n(S)}=\frac{(^7C_3×^6C_3)}{^{13}C_6}=\frac{700}{1716}=\frac{175}{429}$