Counting Question: There are 18 bats, 11 stay in caves, 14 are type I. How many ways are there for the 11 cave dwelling bats to have 9 of type I.

Question

Counting Question: There are 18 bats, 11 stay in caves, 14 are type I.  How many ways are there for the 11 cave dwelling bats to have 9 of type I.

anonymous · Answer

I was thinking (14 choose 9)*(4 choose 2).  i.e first pick the 9 bats of type I, then fill the cave with 2 bats of the 4 of type II.

ganeshie8 · Answer

looks good to me!

anonymous · Answer

OK, its a text book question, and to get there sol. it's (14 C  9)(7 C 2) ?

anonymous · Answer

Which to me have at least 9 type I. but not exactly 9.

ganeshie8 · Answer

how 7 C 2 ?

ganeshie8 · Answer

what does it represent ?

ganeshie8 · Answer

presumably the bats are distinguishable

anonymous · Answer

Don't know.... I think take the 7 remaining bats, 14-9=5 of type I plus 4 type II is 9...  wait... I really don't know

anonymous · Answer

I tried 7 since, 14-11=3 and 4 type II. but that makes no sense.

anonymous · Answer

The text ans.  is  1155

anonymous · Answer

Distinguishable bats give really big numbers...

ganeshie8 · Answer

anonymous · Answer

But why does that make sense?

ganeshie8 · Answer

looks a bit tricky, not really sure...