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Question

On a particular day, seven persons pick six different books, one each, from different counters at a public library. At the closing time, they arbitrarily put their books at vacant counters. The probability that at least four books are at their previous places is 


A
1027!
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B
927!
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C
847!
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D
4077!
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Solution

The correct option is B 927!
Numbe of favourable outcomes = exactly four books are at their previous places + exactly five... + exactly six... + all books...
= 7C4D3+ 7C5D2+ 7C6D1+ 7C7D0, where Dn denotes the derangement of n objects.
=70+21+0+1
=92
Required probability =927!

Mathematics

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