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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

9 years ago

Answers : (1)

879 Points

Dear student,

One digit numbers are 5
two digit numbers can have first digit choosen from 5 digits, the 2nd - from 5, ...the count is 5.5
three digit numbers can be have first digit choosen from 5 digits, the 2nd - from 5 and the third from 4, so 5.5.4
four digit numbers -
five digit numbers -
six digit numbers -
so the count is A=5+5.5+
we 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


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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

9 years ago
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