Question
Match each item given under the column $C_1$ to its correct answer given under the column $C_2.$
There are $3$ books on Mathematics$, 4$ on Physics and $5$ on English. How many different collections can be made such that each collection consists of :
 
$C_1$
 
$C_2$
$(a)$
One book of each subject.
$(i)$ $3968$
$(b)$
At least one book of each subject.
$(ii)$ $60$
$(c)$
At least one book of English.
$(iii)$ $3255$

Answer

 
$C_1$
 
$C_2$
$(a)$
One book of each subject.
$(ii)$ $60$
$(b)$
At least one book of each subject.
$(iii)$ $3255$
$(c)$
At least one book of English.
$(i)$ $3968$
We have $3$ books of mathematics$, 4$ of physics and $5$ on english
  1. One book of each subject $=\ ^3C_1 \times\ ^4C_1 \times\ ^5C_1\ \times = 3 \times 4 \times = 60$
  2. Alleast one book of each subject $= (2^2 - 1) \times (2^4 - 1) \times (2^5 - 1) = 7 \times 15 \times 31 = 3255$
  3. Atlest one book of english $= (2^5 - 1) \times 2^7 = 31 \times 128 = 3968.$ Hence the required matching is

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free