Frank T
2
There are two possible ways a team can be formed, either with only one boy or with no boys (at most one boy means \geq 1 boy)Therefore we can find the number of ways with one boy: ^4 C_1 \times ^6C_3 , and with no boys: ^6C_4 . Adding the two sets of possible teams results in 95. HOWEVER we must also account for all the possible captain selections. Multiplying by 4 accomplishes this and we have 380 for the final answer. Although this is not included in your answer options I am quite confident it is correct.