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Question
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:
| C1 | C2 |
| (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 |
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Solution
| C1 | C2 |
| (a) One book of each subject; | (i) 60 |
| (b) At least one book of each subject: | (ii)3255 |
| (c) At least one book of English: | (iii) 3968 |
Explanation:
We have 3 books of Mathematics, 4 of Physics and 5 on English
(a) One book of each subject = 3C1 × 4C1 × 5C1
= 3 × 4 × 5
= 60
(b) Atleast one book of each subject = (23 – 1) × (24 – 1) × (25 – 1)
= = 7 × 15 × 31
= 3255
(c) Atleast one book of English = (25 – 1) × 27
= 31 × 128
= 3986
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