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by harsh.champ » Mon Feb 08, 2010 3:02 pm
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?

(A)499
(B)500
(C)375
(D)376
(E)501

The OA is D.
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by Ian Stewart » Mon Feb 08, 2010 6:44 pm
Consider first the numbers we could make which are less than 4000. The first digit can be 1, 2 or 3, so we have three choices for the first digit. For the remaining digits we have 5 choices (repetition is allowed), so we can make 3*5*5*5 = 375 such numbers. Since we must also include the number 4000 in our count, there are 375+1 = 376 numbers in total.
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by ajith » Mon Feb 08, 2010 9:29 pm
harsh.champ wrote: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?

(A)499
(B)500
(C)375
(D)376
(E)501

The OA is D.
First digit can be 1,2,3 so 3 ways; second digit can be selected in 5 ways ; third in 5 ways, 4 th in 5 ways and 4000
3*5^3+1 = 376
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by shashank.ism » Wed Feb 10, 2010 12:03 pm
harsh.champ wrote: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?

(A)499
(B)500
(C)375
(D)376
(E)501

The OA is D.
999<I<=4000
digits that can be used 0,1,2,3,4
so total no. of numbers formed 3x5x5x5 +1=376
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by komal » Tue Feb 16, 2010 7:44 pm
harsh.champ wrote: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?

(A)499
(B)500
(C)375
(D)376
(E)501

The OA is D.
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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