Try this beautiful problem from Probability .You may use sequential hints to solve the problem.

## Probability | AMC-8, 2007 |Problem 24

A bag contains four pieces of paper, each labeled with one of the digits 1,2,3 or 4. with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of 3?

- \(\frac{3}{4}\)
- \(\frac{1}{2}\)
- \(\frac{1}{4}\)

**Key Concepts**

probability

combination

Number counting

## Check the Answer

But try the problem first…

Answer: \(\frac{1}{2}\)

AMC-8, 2007 problem 24

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

there are two ways that The combination of digits that give multiples of 3

Can you now finish the problem ……….

Second Hint

The combination of digits that give multiples of 3 are (1,2,3) and (2,3,4)

can you finish the problem……..

Final Step

The combination of digits that give multiples of 3 are (1,2,3) and (2,3,4) . The number of ways to choose three digits out of four is 4. Therefore, the probability is \(\frac{1}{2}\)

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