pet arrangements: There are 15 cats and 15 dogs....

[Clifford]

There are 15 cats and 15 dogs.
a) How many ways could you choose 5 pets?
b) How many ways could you choose 6 pets?
c) How many ways can you choose 7 pets if you pick 5 cats?
d) How many ways can you choose 7 pets if you pick atleast 1 cat?
e) How many ways can you choose 7 pets if you pick atleast 3 cats and 2 dogs?

a) C(30,5)
b) C(30,6)
c) C(15,5) * C(15,2)
d) C(30,7) - C(15,7)
e) C(15,3)*C(15,4) + C(15,4)*C(15,3) + C(15,5)*C(15,2)

Are these arrangements ok? The last few parts were confusing and hard to come up with a solution

 

[soroban]

Hello, Clifford!

Your answers look great to me . . . nice work!