Question

The student population of the leadership club is shown in the table.Grade Level. boys. girls11th grade. 8. 612th grade. 9. 7The teacher will select two 11th grade students and three 12th grade students to attend a conference. How many different groupings are possible

Answer 1

Let:

C1 = Possible combinations for 11th grade

C2 = Possible combintations for 12th grade

TC = Total different groupings

For C1:

$\begin{gathered} C1(n1,k1)=\frac{n1!}{k1!(n1-k1)!} \\ where\colon \\ n1=14 \\ k1=2 \\ so\colon \\ C1=91 \end{gathered}$

For C2:

$\begin{gathered} C2(n2,k2)=\frac{n2!}{k2!(n2-k2)!} \\ where\colon \\ n2=16 \\ k2=3 \\ so\colon \\ C2=560 \end{gathered}$

Therefore:

$\begin{gathered} TC=C1+C2 \\ TC=560+91 \\ TC=651 \end{gathered}$