Hi differentiate,

To divide 8 boys into two unequal sets,

they may be divided into

(a) groups of 1 and 7,

(b) groups of 2 and 6,

(c) groups of 3 and 5

but not groups of 4 and 4 as they would be equal sets

and groups of 0 and 8 is one set.

There are ways to divide into groups of 1 and 7,

since that's the number of ways to choose 1 of the 8,

(leaving 7 in the other group).

There are ways to divide into groups of 2 and 6,

since that's the number of ways to choose 2 of the 8,

(leaving 6 in the other group).

There are ways to divide into groups of 3 and 5,

since that's the number of ways to choose 3 of the 8,

(leaving 5 in the other group).

Remember

(the number of ways to choose 1 from 8) = (the number of ways to choose 7 from 8)

(the number of ways to choose 2 from 8) = (the number of ways to choose 6 from 8)

(the number of ways to choose 3 from 8) = (the number of ways to choose 5 from 8)