## Less Than 500

A three-digit number is drawn at random from all possible 3-digit numbers formed by the digits $1, 2, 3, 4$, and $6$. What is the probability that the number drawn is an even number less than $500$ containing NO digits more than once?
Source: mathcontest.olemisss.edu 9/24/2012

SOLUTION
Possible outcomes: 3-digit numbers formed by the digits $1,2,3,4$, and $6$
$5\times 5\times 5=125$
Desirable outcomes: even numbers less than $500$ containing NO digits more than once
$132\qquad 124\qquad 126$
$142\qquad 134\qquad 136$
$162\qquad 164\qquad 146$
$312\qquad 214\qquad 216$
$342\qquad 234\qquad 236$
$362\qquad 264\qquad 246$
$412\qquad 314\qquad 316$
$432\qquad 324\qquad 326$
$462\qquad 364\qquad 346$
$-\qquad\;\; -\qquad \;\, 416$
$-\qquad\;\; -\qquad \;\, 426$
$-\qquad\;\; -\qquad \;\, 436$
Number of desirable outcomes
$9+9+12=30$
Probability of drawing an even number less than 500 containing no digits more than once
$\frac{30}{125}=.24$

Answer: $0.24$