Of a group of 50 students, 20 are freshmen, 10 are sophomores, 15 are juniors, and 5 are seniors. 5 members must be chosen. How many different committees can there be if there must be exactly one senior and exactly two freshmen on the committee?

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Answer 1 · 2017-01-31T06:53:13

#285000" Committees"#.

#(M_1): 1# Senior Member, out of #5#, can be chosen in #5# ways.

#(M_2): 2# Freshmen Members, out of #20#, can be chosen in

#""_20C_2={(20)(19)}/{(1)(2)}=190# ways.

Note that, so far, #3# Members for the Committee, comprising of

#5# members, have been selected.

#(M_3):# Hence, #2# members are yet to be selected from #25# individuals

#[10"(Sophomores)+"15"(Juniors)]"#, and, this can be done in

#""_25C_2={(25)(24)}/{(1)(2)}=300# ways.

Using the Fundamental Principle of Counting, there can be

#(5)(190)(300)=285000# Committees.