Four boys and four girls try out for a school musical. The number of ways that the director can select a male lead singer, a female lead singer, and 3 students to provide vocal back-ups is
my work:$${_4C_1} \times {_4C_1} \times {_6C_3}$$
That would be $4\times 4\times 20 = 320$ ways
is this correct?
Your answer is correct.
The ways of selecting a male lead singer out of $4$ male singers $\large ={^4C_1}$
The ways of selecting a female lead singer out of $4$ female singers $\large ={^4C_1}$
Number of left singers $4+4-2=6$. The ways of selecting $3$ students out of $6$ for vocal back ups $$={^6C_3}$$
The total ways of selecting musical team $$={^4C_1}\times {^4C_1}\times {^6C_3}=320$$