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Q.

There are 6 different balls and 6 different boxes of the colour same as of  the colour of
ball then choose  correct statement (s) 

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a

The number of ways in which no ball goes in the box of the own colour is 265

b

The number of ways in which atleast 4 balls goes into their own boxes is 16

c

The number of ways in which atmost 2 balls goes into their own boxes is 664

d

The number of ways in which exactly 5 balls goes into their own boxes is 0

answer is A, B, C, D.

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Detailed Solution

6!(12!13!+14!15!+16!)=265

Either four balls or all balls go into correct boxes=16
Either all balls go incorrect or exactly one ball go into correct box or two balls go into  265+6C1.5!(12!13!+14!15!)+6C2.9=664 correct

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