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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?

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#### Solution

The number of ways of selecting 2 maths books from 9 maths books is 9C_{2}.

Similarly number of ways of selecting Economics, and History books are 8C_{2} and 7C_{2}.

∴ 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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