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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?

in Combinatory by Boss (17.7k points)
edited by | 342 views
is it 56 ?
Can you explain as well ?
we have to choose 5 books in which no 2 are adjacent rt remaining  7 books means 8 places .. where we arrange(select is more suitable ) these 5 books 8c5 =56 ( girl boys , no two girls are together kind of problem i think )
Nice. I was trying to think in terms of number of selecting the way we can pick book. This approach is clearly better.
yes you can that way but bit lengthy and may be one of case miss
@Sonam, how with remaining 7 books it cud mean 8 places??Can u please elaborate on ur explanation part??
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.
Yes Sonam it's 56. Thanx a lot. Nice analogy used.

1 Answer

+10 votes
Best answer

ans should be 56 .

by Boss (17.1k points)
selected by
@Sonam, Thanks a lot. :)
@Sonam, but where do d remaining 5 go?
8 places we select 5 books right
Cant books shuffle around ? they should be identical i think.
@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. :)
@s9k96 , i think we have to select so it mean lot rt ..

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