Question

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
(i) one book of each subject,
(ii) atleast one book of each subject,
(iii) atleast one book of literature.

Answer 1

(i) ${}^3{C}_1$ x ${}^4{C}_1$ x ${}^5{C}_1$ = 3.4.5 = $60$
(ii) ($2^3-1$) ($2^4-1$) ($2^5-1$) = 7 x 15 x 31 = $3255$
(iii) $2^3$. $2^4$.($2^5-1$) = 8 x 16 x 31 = $3968$.