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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
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. Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi sagarsingh24.iitd@gmail.com
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.
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi sagarsingh24.iitd@gmail.com
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi
sagarsingh24.iitd@gmail.com
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