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

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About mvtrinh

Retired high school math teacher.
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