There are 3 books of mathematics, 4 of science, and 5 of literature. How many different collections can be made such that each collection consists of one book of each subject, at least one book of each subject, at least one book of literature.

Explanation

(i) One book of each subject is selected.
So, number of ways of selections `=.^(3)C_(1)xx .^(4)C_(1)xx .^(5)C_(1)`
`=3xx4xx5=60`
(ii) At least one book of each subject is selected.
Number of ways of ways of selection of at least one mathematics book `=3^(3)-1=7`
Number of ways of selection of at least one science book
`=2^(4)-1=15`
Number of ways of selection of at least one literature book
`=2^(5)-1=31`
So, total number of ways of selection `=7xx15xx31=3255`
(iii) At least one book of literature is selected.
So, we can select any number of mathematics and science books including zero selection.
So, number of ways of selection `=2^(3)xx2^(4)xx(2^(5)-1)`
`=128xx31=3968`