Overpowering tens unit

Probability Level 1

How many positive 2 digit numbers are there, such that the units digit is strictly smaller than the tens digit?

Details and assumptions

The number $12=012$ is a 2-digit number, not a 3-digit number.

The answer is 45.

1 solution

Arron Kau Staff
May 13, 2014

If the tens digit is $k$ , then the units digit can be $0, 1, 2, \ldots k-1$ , so there are $k-1 - 0 + 1 = k$ possibilities. Since $k$ can range from 1 to 9, by the rule of sum, there are $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$ such values.

Overpowering tens unit

The answer is 45.

1 solution

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