Are you sure you want ONLY the coefficient of b? If you expand this, you will have b in 3 of 4 terms.
According to Pascal's Triangle, the coefficients of (a+b)^4 are as follows:
1
1 2 1
1 3 3 1
1 4 6 4 1
So (a+b)^4 would be 1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
Here, you want (3 + b)^4. Here's what that looks like:
3^4 + 4[3^3*b] + 6[3^2*b^2] + 4[3*b^3] + 1[b^4]
Which coeff did you want?
The possibilities are:
bbbb
bbbg
bbgg
bggg
This shows that there is a 1 in 4 chance of having three boys and one girl
So the answer could be 1/4 or a 25% chance
Technically nothing times 3 get you 16 but 3 times 5 equals 15 which is the closest answer but the answer would be 5.3
