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Question
In how many different ways, 2 Mathematics, 2 Economics and 2 History books can be selected from 9 Mathematics, 8 Economics and 7 History books?
Solution
The number of ways of selecting 2 maths books from 9 maths books is 9C2.
Similarly number of ways of selecting Economics, and History books are 8C2 and 7C2.
∴ Total number of selecting books.
`= 9"C"_2 xx 8"C"_2 xx 7"C"_2 = (9 xx 8)/(2 xx 1) + (8xx7)/(2xx1) + (7 xx 6)/(2 xx 1)`
= 9 × 4 + 4 × 7 + 7 × 3
= 36 + 28 + 21
= 85
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