There are 3 books of Mathematics, 4 of Physics and 5 of English. How many different collections can be made such that each consists at least one book of each subject ?

Explanation

There are three books of Mathematics 4 of Physics and 5 on English.
(i) One book of each subject `= ""^(3)C_(1) xx ""^(4)C_(1) xx ""^(5)C_(1)`
`= 3 xx 4 xx 5 = 60`
(ii) Atleast one book of each subject `= (2^(3) - 1) xx (2^(4) - 1) xx (2^(5) - 1)`
`= 7 xx 15 xx 31 = 3255`
(iii) Atleast one book of English = selection based on following manner
`{:("English book", 1, 2, 3, 4, 5),("Others", 11, 10, 9, 8, 7):}`
`= (2^(5) - 1) xx 2^(7)`
`= 128 xx 31 = 3968`