Answer:
bbbb,
bbbg, bbgb, bgbb, gbbb,
bbgg, bgbg, bggb, gbgb, gbbg, ggbb,
bggg, gbgg, ggbg, gggb,
gggg
Step-by-step explanation:
3 children: bbb, bbg, bgb, gbb, bgg, gbg, ggb, ggg
4 children: bbbb, bbbg, bbgb, bgbb, gbbb, bbgg, bgbg, bggb, gbgb, ggbb, bggg, gbgg, ggbg, gggb, gggg
You need to take a methodological approach;
The 2 easiest are the possibility of all boys and all girls;
Then consider 3 boys and 1 girl:
bbbg, bbgb, bgbb, gbbb
Then 2 boys and 2 girls:
bbgg, bgbg, bggb, gbgb, gbbg, ggbb
Lastly, 1 boy and 3 girls:
bggg, gbgg, ggbg, gggb
In total, there are 16 possibilities
P.S. interesting to note is that the number of possibilities here follows the pattern of Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
The last row is relevant here;
There is 1 possibility where there are 4 boys;
There are 4 possibilities (in terms of the order of birth) where there are 3 boys and 1 girl;
There are 6 possibilities where there are 2 boys and 2 girls
There are 4 possibilities where there is 1 boy and 3 girls;
There is 1 possibility where there are 4 girls;
The pattern ∴ is 1 4 6 4 1, as the 5th row of Pascal's triangle reads;
If your talking about 3 children, it would match the 4th row of Pascal's triangle;
So, 1 possibility of 3 boys;
3 possibilities of 2 boys and 1 girl;
3 possibilities of 1 boy and 2 girls;
And 1 possibility of 3 girls;
If your talking about 10 children, it would match the 11th row of Pascal's triangle.
(Maths can be so cool XD)
= 6.7082