freshmen, sophomores and an advisor

[emilyrua]

Hi. I just want to check that I did these correctly, since I missed a class...

A group consists of 55 freshmen, 44 sophomores and 1 advisor.

a) How many ways can a group of 4 people be selected?
using nCr on my TI-83 calculator (n=100, r=4) I got 3,921,225

b) How many such groups consist of all freshmen?
again using nCr (n=55, r=4), I got 341,055

c) How many such groups consist of 2 freshmen & 2 democrats?
nCr (n=44, r=2) + nCr (n=55, r=2) = 946 + 1485 = 2431

d) How many such groups would the advisor be part of?
nCr (n=99, r=3) = 156,849

Please let me know if you spot any glaring errors here, or if I misunderstood and used the wrong formula. Thanks!

 

[marcmtlca]

I think c) may be wrong. It seems to me that you should multiply and not add these two quantities... id double check it, i might be wrong

 

[soroban]

Hello, Emily!

marcmtica is absolutely correct . . . multiply in part (c) . . .

c) How many such groups consist of 2 freshmen and 2 sophomores?

\(\displaystyle _{55}C_2\,\)X\(\displaystyle \,_{44}C_2\)