Arithmetic Ability
Permutations and Combinations

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Q.

The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :

View Answer

Correct choice: C

Explanation:

Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where 0≤x,y,z≤9. Let us first count the numbers in which 8 occurs exactly once. Since 8 can occur atone place in 3C1 ways. There are 3 x 9 x 9 such numbers.Next, 8 can occur in exactly two places in 3C2×9 such numbers. Lastly, 8 can occur in all three digits in one number only. Hence, the number of times 8 occur is 1×(3×92)+2×(3×9)+3×1 = 300
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