how many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
The number of such 3-digit numbers is 20.
Quick Scoop: Core Idea
To be divisible by 5, a number must end in 0 or 5.
Here, the available digits are 2, 3, 5, 6, 7, and 9, so the only possible last
digit is 5.
So we fix the units (last) place as 5.
- Units place: 5 (only 1 option).
- Remaining digits for hundreds and tens places: 2, 3, 6, 7, 9 (5 digits left).
Now we must form a 2-digit number (hundreds and tens) from these 5 digits, with no repetition.
- Ways to choose the hundreds digit: 5 options.
- After choosing the hundreds digit, ways to choose the tens digit: 4 options.
Total 3-digit numbers:
5×4×1=205\times 4\times 1=205×4×1=20
So, 20 different 3-digit numbers can be formed from 2, 3, 5, 6, 7, and 9 that are divisible by 5 with no repeated digits.
Mini Table: Position Choices
| Position | Available digits | Number of choices |
|---|---|---|
| Hundreds | 2, 3, 6, 7, 9 | 5 |
| Tens | Remaining after choosing hundreds | 4 |
| Units | 5 (fixed, to be divisible by 5) | 1 |
Example View
A few sample numbers from the 20:
- 235, 275, 295
- 365, 695
- 975, 765
Each uses digits from the set, ends in 5, and has no repeated digit.
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Learn how to find how many 3-digit numbers can be formed from the digits 2,
3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is
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