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46) A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen?

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is it 56 ?
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Can you explain as well ?
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we have to choose 5 books in which no 2 are adjacent rt ..so remaining  7 books means 8 places .. where we arrange(select is more suitable ) these 5 books ..so 8c5 =56 ( girl boys , no two girls are together kind of problem i think )
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Nice. I was trying to think in terms of number of selecting the way we can pick book. This approach is clearly better.
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yes you can that way but bit lengthy and may be one of case miss
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@Sonam, how with remaining 7 books it cud mean 8 places??Can u please elaborate on ur explanation part??
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If you have two books, then there are 3 places.

o | o | o

here "|" marks the books and "o" empty spaces. By the same logic, when you have 7 books there are 8 empty spaces.
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Yes Sonam it's 56. Thanx a lot. Nice analogy used.

ans should be 56 .

by Boss (17.1k points)
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@Sonam, Thanks a lot. :)
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@Sonam, but where do d remaining 5 go?
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8 places we select 5 books right
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Cant books shuffle around ? they should be identical i think.
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@Sonam, I now got ur point. Actually I was taking 8 places to be books and getting confused. So now it is clear. In this way d total shall be 12. Actually u've made d question easier and simplified it with a little bit change. Thanks a lot. :)
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@s9k96 , i think we have to select so it mean lot rt ..