Question

A committee consists of eight students and five faculty. how many possible five-person subcommittees are there? how many that contain exactly three students? how many that contain at least three students

Answer 1

A committee consists of eight students and five faculty.

how many possible five-person subcommittees are there?

Answer: We have a total of 13 people from whom we have to choose 5-person subcommittee.

Therefore, the number of possible ways is:

`\binom{13}{5}=1287` ways

how many that contain exactly three students?

Answer: The number of ways that will contain exactly three students is:

`\binom{8}{3} * \binom{5}{2} = 56 * 10 =560` ways

how many that contain at least three students

Answer: The number of ways that will contain at least three students is:

`\binom{8}{3} * \binom{5}{2} +\binom{8}{4} * \binom{5}{1} +\binom{8}{5} * \binom{5}{0}`

`56 * 10 + 70 * 5 + 56 * 1 = 560+350+56 = 966` ways