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Number of 4-digit numbers not greater than 4000

The question given below appeared in CAT 2008. One could get the answer to the question in a little less than 2 minutes. What is essential is a little care to ensure that you do not make any error in oversight (commonly referred as "silly mistake"). The common error in oversight made is not reading the question correct. So, do not lose focus while reading the question. Understand it properly and then answer the question.

Question 7

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

(1) 499
(2) 500
(3) 375
(4) 376
(5) 501

Correct Answer is 376 - Choice (4)

Explanation

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 * 5 * 5 * 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.

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