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Homework Statement
How many times does digit 5 occur in numbers fro 0-1000.
Homework Equations
The Attempt at a Solution
This is what i have done.
Total (1,2,3) digit numbers which have digit 5 occurring once in them are-:
[itex] 3.^9C_1.^9C_1 = 243 [/itex]
Total numbers with 5 occurring twice are [itex] ^9C_1 = 9 [/itex]
So, digit 5 occurs 9*2=18 times
Total Numbes with 5 occurring thrice= 1
So digit 5 occurs 3*1=3
Total times digit 5 occurs is 243+18+1=264
Is this correct, specially regarding repetitions or exclusions which i may have made?