Answer
$\displaystyle \frac{1}{7}$
Work Step by Step
$P(E)=\displaystyle \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$
$n(S)=C(10,5)=252$
$E$ = $(2$ of 4 reds) AND (1 of 3 greens) AND (1 of 2 whites) AND (1 of 1 purple)
$n(E)=C(4,2)\cdot C(3,1)\cdot C(2,1)\cdot C(1,1)=6\cdot 3\cdot 2\cdot 1=36$
$P(E)=\displaystyle \frac{36}{252}=\frac{1}{7}$