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Question

There are counters available in x different colours. The counters are all alike except for the colour. The total number of arrangements consisting of y counters, assuming sufficient number of counters of each colour, if no arrangement consists of all counters of the same colour is :

A
xyx
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B
xyy
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C
yxx
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D
yxy
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Solution

The correct option is A xyx
For each of y counters there could be x possibilities,
Total=x×x×x........y times=xy
But there will be x cases, when all counters will be of same colour, so we can't have such arrangement,
Total=xyx
Hence, (A)

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