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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.

If atleast one cap has to be distributed and the caps have to be arranged such that any box can have a maximum of one cap only, in how many ways can arrange the caps among 5 boxes?

A
1
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B
16
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C
1545
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D
none of these
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Solution

The correct option is C 1545
I cap can be selected in 5C1 ways.
Now this selected cap can be arranged in 5 boxes in 5P1 ways.
Again 2 caps can be selected in 5C2 ways.
Now, these selected caps can be arranged in 5 boxes in 5P2
ways and so on.
Hence the required number of ways
5C1×5P1+5C2×5P2+5C3+5C4×5P4+5C5×5P5=25+200+600+600+120=1545

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