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Question

There are 5 different caps c1,c2,c3,c4 and c5 and 5 different boxes B1,B2,B3,B4 and B5. The capacity of each box is sufficient to accomodate all the 5 caps.

In how many arrangements does B1 have cap C1?

A
5!
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B
54
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C
5P4
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D
none of these
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Solution

The correct option is B 54
Required number of arrangements =5×5×5×5=625
Since we fix cap C1 in box B1 then we arrange the remaining 4 caps in any of the 5 boxes
Alternatively: Total number of arrangements =55
Number of arrangements in which B1 have cap C1=555=54

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