Ordered Balls

Probability Level 3

A bag contains $150$ balls numbered $1$ through $150$ . Three balls are drawn and placed on the table. The probability that the balls were drawn in increasing order can be expressed as $\frac{a}{b}$ where $a$ and $b$ are coprime positive integers. What is the value of $a + b$ ?

Details and assumptions

The balls are drawn in increasing order if each subsequent ball is a higher number. As an explicit example, drawing balls $1, 10, 100$ in that order is considered an increasing order.

The answer is 7.

1 solution

Arron Kau Staff
May 13, 2014

For any 3 balls, there are $3! = 6$ ways they can be arranged, one of which is in increasing order, so the probability that the balls we draw are in order is $\frac{1}{6}$ . Hence $a + b = 1 + 6 = 7$ .

Ordered Balls

The answer is 7.

1 solution

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