MediumMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalBoard ExamA-LevelIB
How many 3-digit numbers have three different digits? How many of them are odd?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
How many -digit numbers have three different digits? How many of them are odd?
Need a reminder? The key ideaShow
If a task can be done in ways or in other ways, with no way in both, it can be done in ways. Stages one after another multiply; separate cases add. Fill a place that has a rule first.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. All of them. Hundreds: ways (not ). Tens: ways (any digit but that one). Units: ways. So .
Step 2. The odd ones. Units: odd digits. Hundreds: not and not the units digit, so . Tens: . So .
Answer: numbers, of which are odd.
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