Question

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

Solution

Correct option is

300

Since 3 does not occur in 1000, we have to count the number of times 3 0ccurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form 0 ≤ xyz ≤ 9. Let us first count the number in which 3 occurs exactly once. Since 3 can occurs at one place in 3C1ways, there are 3C(9 × 9) = 3 × 92 such numbers. Next, 3 can occur in exactly two places in (3C2)(9) = 3 × 9 such numbers. Lastly, 3 can occur in all three digits in one number only. 

Hence, the number of times 3 occur is 

     .

SIMILAR QUESTIONS

Q1

The term digit of 1! + 2! + 3! + … + 49! Is

Q2

Four dice are rolled. The number of possible outcomes in which least one die shows 2 is

Q3

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that P  Q = Ï• is

Q4

Let E = {1, 2, 3, 4} and F = {ab}. then the number of onto functions from E to F is

Q5

The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

Q6

The range of function 

Q7

The number of ways of arranging letters of the word RACHIT so that the vowels are in alphabetical order is

Q8

A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

Q9

The number of ways in which a mixed double game can be arranged from amongst 9 married couple if no husband and wife play in the same game is 

Q10

The number of positive integers n such that 2n divides n! is