Please Help ASAP Combinations :(

10 freshmen, 10 sophomores, 8 juniors, and 7 seniors are eligible to be on a committee.

In how many ways can a dance committee of 17 students be chosen?

In how many ways can a dance committee be chosen if it is to consist of 5 freshmen, 4 sophomores, 6 juniors, and 2 seniors.

i) 35C17

ii)31116960

Step-by-step explanation:

i)total number of eligible are 35

now ways of chosing 17 from 35 is 35C17,

ii)Total ways of selecting 2 seniors from 7 is 7C2

and Total ways of selecting 6 juniors from 8 is 8C6

ways of selecting 4 sopho from 10 is 10C4

ways of selecting 5 freshman from 10 is 10C5

now, total way of selection come to be

10C5×10C4×8C6×7C2

i.e,252×210×28×21

i.e, 31116960

✌️:)