There are three books of physics, four of chemistry and five of mathematics. How many different collections can be made such that each collection consists of
(i) one book of each subject
(ii) atleast one book of each subject.
(iii) atleast one book of mathematics.

Explanation

(i) `.^(3)C_(1)xx.^(4)C_(1)xx.^(5)C_(1)=3xx4xx5=60`
(ii) `(2^(3)-1)xx(2^(4)-1)xx(2^(5)-1)=7xx15xx31=3255`
(iii) `(2^(5)-1)xx2^(7)=31xx128=3968`