On a particular day six persons pick six different books one each from different counters at a public library - Maths - Probability

Question

On a particular day six persons pick six different books one each
from different counters at a public library At closing time they
arbitrarily put their books to the vacant counters Then find the
probability that exactly two books are at their previous places

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Formula for dearrangements of n objects i
e if there are 'n' objects and 'n' slots and no object goes to correct slot, is given by:Number of ways=n!1-11!+12!-13!+
Here we have 6 books out of which we to dearrange 4 books while 2 of booksshould go to correct place
⇒Required Number of ways=6C2×6-2!1-11!+12!-13!+14!=6×52×1
4!1-1+12-16+124=15
242-246+2424=1512-4+1=135Total number of ways=6!=720⇒Required Probability=135720=316 Answer

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On a particular day six persons pick six different books one each from different counters at a public library . At closing time they arbitrarily put their books to the vacant counters . Then find the probability that exactly two books are at their previous places