John's Billard Balls

Discrete Mathematics Level 3

John has a bag of colored billiard balls which are labeled with the numbers $1, 2, 3, 4, 5, 6$ . He reaches into the bag, draws out a ball, records down the number and then places the ball back in the bag. He does this a total of 4 times (hence has 4 numbers). The probability that at least $2$ of the numbers are equal is $\frac{a}{b}$ , where $a$ and $b$ are positive, coprime integers. What is the value of $a + b$ ?

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John's Billard Balls

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.