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Question
How many different selections of 5 books can be made from 12 different books if, Two particular books are never selected?
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Solution
Two particular books are never selected.
Since two books are never selected.
The total number of books is 10.
∴ The number of ways of selecting 5 books from 10 books
= 10C5
= `(10!)/(5! xx (10 - 5)!)`
= `(10!)/(5! xx 5!)`
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5! xx 5!)`
= `(10 xx 9 xx 8 xx 7 xx 6)/(5!)`
= `(10 xx 9 xx 8 xx 7 xx 6)/(5 xx 4 xx 3 xx 2 xx 1)`
= 2 × 9 × 2 × 7
= 252 ways
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