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HOW MANY TIMES 5 WILL COME FROM 1 TO 1000
Answers
Answer:
200 times
Explaination:
To Find: No of time digit 5 is used between 1 & 1000
⇒ 200 times
∴ 20 times digit 5 is used between 1 and 100.
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By adding the number of times the digit 55 occurs in each position, you have counted each number in which 55 appears exactly two times twice and each number in which 55 appears exactly three times thrice, once for each position in which it occurs, which is why your method produces the right answer.
Alternate Method: We want to count the number of times the digit 55 appears in the list of positive integers from 11 to 10001000. Thus, we need to count each integer in which the digit 55 appears exactly once once, each integer in which the digit 55 appears exactly two times twice, and each integer in which the digit 55 appears exactly three times thrice.
Numbers in which the digit 55 appears exactly once: There are three ways to choose the position of the digit 55. Since we cannot use 55 in the remaining positions, there are nine choices for each of the remaining digits. Hence, there are
(31)92
(31)92
such numbers.
Numbers in which the digit 55 appears exactly twice: There are (32)(32) ways to choose the positions of the digit 55. Since we cannot use 55 in the remaining position, there are nine choices for the remaining digit. Hence, there are
(32)9
(32)9
such numbers.
Numbers in which the digit 55 appears exactly thrice: There is only one such number, namely 555555.
Total: The number of times the digit 55 appears when listing each integer from 11 to 10001000 is
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