Answer
3
Work Step by Step
Use the formula of permutation:.You have two permutation problems:$_{5}$$P_{3}$ and $_{5}$$P_{2}$. Solve each one separately and divide the solutions in the end:
--> $_{n}$$P_{r}$=$\frac{n!}{(n-r)!}$
$_{5}$$P_{3}$=$\frac{5!}{(5-3)!}$
$_{5}$$P_{3}$=$\frac{5!}{2!}$
$_{5}$$P_{3}$=$\frac{5*4*3*2*1}{2*1}$
$_{5}$$P_{3}$=60
--> $_{n}$$P_{r}$=$\frac{n!}{(n-r)!}$
$_{5}$$P_{2}$=$\frac{5!}{(5-2)!}$
$_{5}$$P_{2}$=$\frac{5!}{3!}$
$_{5}$$P_{2}$=$\frac{5*4*3*2*1}{3*2*1}$
$_{5}$$P_{2}$=20
Divide the solutions: 60÷20=3.So $_{5}$$P_{3}$ $\div$ $_{5}$$P_{2}$=3