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 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 - 5.5.4.3
five digit numbers - 5.5.4.3.2
six digit numbers - 5.5.4.3.2.1
so the count is A=5+5.5+5.5.4.3+5.5.4.3.2+5.5.4.3.2.1
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 5.5.4.2.

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