SATHEE: Permutations And Combinations Question 36

Permutations And Combinations Question 36

Question: The number of times the digit 5 will be written when listing the integers from 1 to 1000 is

Options:

A) 271

B) 272

C) 300

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

Since 5 does not occur in 1000, we have to count the number of times 5 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form $ xyz,\ 0\le x,\ y,\ z\le 9 $ . The numbers in which 5 occurs exactly once $ ={{(}^{3}}C_1)\ .\ 9\times 9=243 $ . The numbers in which 5 occurs exactly twice = $ {{(}^{3}}C_2.9)=27 $ The numbers in which 5 occurs in all three digits $ =1 $ Hence, the number of times 5 occurs is $ 1\times 243+2\times 27+3\times 1=300 $ .

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Permutations And Combinations Question 36

Question: The number of times the digit 5 will be written when listing the integers from 1 to 1000 is

Options:

Answer:

Solution:

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