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:
[tex]\binom{13}{5}=1287[/tex] ways
how many that contain exactly three students?
Answer: The number of ways that will contain exactly three students is:
[tex]\binom{8}{3} \times \binom{5}{2} = 56 \times 10 =560[/tex] ways
how many that contain at least three students
Answer: The number of ways that will contain at least three students is:
[tex]\binom{8}{3} \times \binom{5}{2} +\binom{8}{4} \times \binom{5}{1} +\binom{8}{5} \times \binom{5}{0} [/tex]
[tex]56 \times 10 + 70 \times 5 + 56 \times 1 = 560+350+56 = 966[/tex] ways
