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.
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.
looks good to me!
OK, its a text book question, and to get there sol. it's (14 C 9)(7 C 2) ?
Which to me have at least 9 type I. but not exactly 9.
how 7 C 2 ?
what does it represent ?
presumably the bats are distinguishable
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
I tried 7 since, 14-11=3 and 4 type II. but that makes no sense.
The text ans. is 1155
Distinguishable bats give really big numbers...
https://www.wolframalpha.com/input/?i=%2811+choose+9%29*%287+choose+2%29
But why does that make sense?
looks a bit tricky, not really sure...
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