The probability that a family with 6 children has exactly four boys is:  Choices
A) 1/3  B) 1/64  C) 15/64  D) 3/8  E) none of the above
Now let's find the # of combinations where there's a BGB combination. Let the sequence of BG=A:   BBAA   BAAB   BABA   ABBA   ABAB   AABB   So there are 6 combinations here. But since BG can also be GB, we have to multiply by 2. We have to multiply by another 2 because there are 2 As. Therefore, there are 6x2x2=24 combinations.   We also have to include the instances where GG occurs at the end or the front, that is:   GGBBBB   BBBBGG   (all the other instances such as BBGGBB have been taken care of in the calculation at the top)   So we have   24+2= 
<gadget id="calculator">  24+2</gadget>
<output>26</output>
26 possibilities of 4 boys and 2 girls.   The total number of possibilities is 2^6=64. Therefore, the probability is 26/64, which is 13/32. The answer is none of the above
<result>E</result>
The probability that a family with 6 children has exactly four boys is: