Help Please
Student Congress has six members who are seniors and four members who are juniors. At Spring Premiere for prospective students, one of the juniors greets prospective students, one works at the registration table, and a third gives a welcome to the campus greeting. One of the seniors introduces the dean of students, another introduces the academic vice-president, and the third discusses how to apply for financial aid. How many ways can these assignments be made?

Question

Help Please
Student Congress has six members who are seniors and four members who are juniors. At Spring Premiere for prospective students, one of the juniors greets prospective students, one works at the registration table, and a third gives a welcome to the campus greeting. One of the seniors introduces the dean of students, another introduces the academic vice-president, and the third discusses how to apply for financial aid. How many ways can these assignments be made?

ybarrap · Answer

There are $\large \binom{6}{3}$ ways for seniors to be assigned and $\large \binom{4}{3}$ ways for juniors to be assigned, therefore, the total number of ways assignments can be made is $\large \binom{6}{3}\times\binom{4}{3}=80$

Does this make sense?