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?

Question

3454 views around the world

You can reuse this answer
Creative Commons License

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.