Answer
300
Work Step by Step
A)Find $_{6}$C$_{4}$:
$_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$
$_{6}$C$_{4}$=$\frac{6!}{4!(6-4)!}$ -simplify like terms-
$_{6}$C$_{4}$=$\frac{6!}{4! (2!)}$ -write using factorial-
$_{6}$C$_{4}$=$\frac{6*5*4*3*2*1}{(4*3*2*1)(2*1)}$ -simplify-
$_{6}$C$_{4}$=15
B)There are 3 more questions to be answered and 6 questions left.
C)Find $_{6}$C$_{3}$ from information from B.
$_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$
$_{6}$C$_{3}$=$\frac{6!}{3!(6-3)!}$ -simplify like terms-
$_{6}$C$_{3}$=$\frac{6!}{3! (3!)}$ -write using factorial-
$_{6}$C$_{3}$=$\frac{6*5*4*3*2*1}{(3*2*1)(3*2*1)}$ -simplify-
$_{6}$C$_{3}$=20
D.Multiply the results from A and C using the multiplication counting principle:
15$\times$20=300
The answer is 300.
