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How is it coming 92? The result of the calculation mentioned is 90


How?

The calculation gives 92, not 90.

8 + 28 + 56 = 92.
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Choose any boy without loss of generality . Then choose a subset of the other 7 boys to be in his set

However , not all 7 other boys and not a subset of size 3

2^7 - 1 -7c3= 128 - 1 - 35= 92
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How many ways can eight boys be distributed into two spots ?

2^8 = 256.

This, however, includes two cases where all the boys are one location and none are in the other, so subtract 2 = 254

The above also includes an equal distribution or four and four, which is disallowed by the question stem and need to be subtracted.

Four boys can be selected in 8!/4!4! = 70 ways. The other four boys automatically fall from the calculation as well.

Preliminary result: 256-2-70 = 184, which is the number of ways the boys can be distributed in two unequal sets assuming, however, that the two sets are distinguished from each other for reasons other than their number, which is not supported by anything in the question stem so this number needs to be divided by two:

184/2 = 92
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