Out of 3 books on Economics, 4 books on Political Science and 5 books on History, how
many collections can be made if each collection consists of
(i) exactly one book on each subject? (ii) atleast one book on each subject?
the first parce
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60 Ways exactly one book on each subject , 3255 ways atleast one book on each subject
Step-by-step explanation:
Economics = 3 books
Political science = 4 books
History = 5 Books
(i) exactly one book on each subject
= ³C₁ * ⁴C₁ * ⁵C₁
= 3 * 4 * 5
= 60 Ways
(ii) atleast one book on each subject
Economics = ³C₁ + ³C₂ + ³C₃ = 3 + 3 + 1 = 7 ways
Political science ⁴C₁ + ⁴C₂ + ⁴C₃ + ⁴C₄ = 4 + 6 + 4 + 1 = 15 ways
History ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅= 5 + 10 + 10 + 5 + 1 = 31 ways
7 * 15 * 31
= 3255 ways
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