Probability

[hmd128]

A jungle contains 10 bears, 12 lions, and 5 foxes. From these animals, a group of 7 will be selected. How many distinct groups are possible if:

a) There are two bears, 3 lions, and 2 foxes.

b) Exactly 4 lions


These are what I have, but I feel it's super wrong:
a)
b)

 

[LCKurtz]

a) looks fine. But for b) selecting 4 from 12 is good. But the rest is easier. Just think about selecting the remaining 3 from the remaining total of other animals.

 

[hmd128]

a) looks fine. But for b) selecting 4 from 12 is good. But the rest is easier. Just think about selecting the remaining 3 from the remaining total of other animals.

Thanks for the reply! It makes sense.

 

[nasi112]

Thanks for the reply! It makes sense.

LCKurtz meant

[MATH]{12 \choose 4}{15 \choose 3} = 225225[/MATH]