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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 accommodate all the 5 caps. If B1 and B5 have the caps C1 and C5 among themselves, in how many ways can you arrange the caps among the 5 boxes?

A
400
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B
485
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C
500
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D
365
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Solution

The correct option is C 500
B1 and B5 can be filled up in 2 × 2 = 4 ways and B2,B3,B4 can be filled up in =5×5×5=125 ways.
Hence the required number of ways =4×125=500

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