Because we need 6 books, we want to choose 2 books from each the followings:
-- 5 books of Mathematics,
-- 4 books of Physics, and
-- 2 books of Biology.
How many possibilities do we have?
We have:
C(2,5) = 10 possibilities to choose 2 books among the 5 books
of Mathematics.
C(2,4) = 6 possibilities to choose 2 books among the 4 books
of Physics.
C(2,2) = 1 possibility to choose 2 books among the 2 books
of Biology.
The total of possibilities is: 10 x 6 x 1 = 60 possibilities
to choose 3 books among 11 books.
Remarks:
1. If we have to choose 2 whatever books from the 11 books, the number
of possibilities is : C(2,11) = 11!/2! (11 - 2)! = 11!/2! 9! =
10 x 11 /2 = 55 possibilities only.
2. Choosing books of Mathematics do not affect the choice of books
of Physics or Biology. We say hat the three choices of books are
independent events. Generally, the number of possibilities for
independent events is the product of the possibilities for
each event.
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