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```        find the number of positive integers which can be formed by any number of digits 012345 but using only once. how many of these integers will be greater than 3000
```
6 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
One digit numbers are 5two digit numbers can have first digit choosen from 5 digits, the 2nd - from 5, ...the count is 5.5three digit numbers can be have first digit choosen from 5 digits, the 2nd - from 5 and the third from 4, so 5.5.4four digit numbers - 5.5.4.3five digit numbers - 5.5.4.3.2six digit numbers - 5.5.4.3.2.1so the count is A=5+5.5+5.5.4.3+5.5.4.3.2+5.5.4.3.2.1we extract the count of 1,2, 3digit numbers - so we totally extract B=5+5.5+5.5.4. the  number we look for is A-B - the number of number that are in the  interval 1000 to 3000 that are formed from the above digits. Notice that  we can't form a the number 3000.the first digit is 1 or 2. Then we  have 5 possibilities for the second digit, 5 for the 3rd, 4 for the  fouth. Totally 5.5.4 multiplied by 2, so 5.5.4.2.

All the best.
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Sagar Singh
B.Tech, IIT Delhi
sagarsingh24.iitd@gmail.com

```
6 years ago
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