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13 Jul 2019, 05:41
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D
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Difficulty:
65%
(hard)
Question Stats:
50% (01:03) correct
50%
(01:53)
wrong
based on 10
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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
(1) 499
(2) 500
(3) 375
(4) 376
(5) 501
The minimum number that can be formed is 1000 and
the maximum number that can be formed is 4000.
As 4000 is the only number in which the first digit is 4,
first let us calculate the numbers less than 4000 and
then we will add 1 to it.
First digit can be 1, 2 or 3.
Remaining 3 digits can be any of the 5 digits.
Total numbers that can be formed, which are less
than 4000 = 3 × 5 × 5 × 5 = 375
Total numbers that satisfy the given condition
= 375 + 1 = 376
the maximum number that can be formed is 4000.
As 4000 is the only number in which the first digit is 4,
first let us calculate the numbers less than 4000 and
then we will add 1 to it.
First digit can be 1, 2 or 3.
Remaining 3 digits can be any of the 5 digits.
Total numbers that can be formed, which are less
than 4000 = 3 × 5 × 5 × 5 = 375
Total numbers that satisfy the given condition
= 375 + 1 = 376
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13 Jul 2019, 05:51
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All numbers greater than 999 but not greatest than 4000 are 4 digit numbers
From 1000-3999,
We have 3 options for the first digit (1,2,3),
5 options for each of the 2nd 3rd and 4th digits (0-4)
So total from 1000-3999 = 3*5*5*5 = 375
Added to this we can also have 4000
Therefore the number of 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 = 375+1 = 376
Answer is (D)
Hit Kudos if this helped!
Posted from my mobile device
From 1000-3999,
We have 3 options for the first digit (1,2,3),
5 options for each of the 2nd 3rd and 4th digits (0-4)
So total from 1000-3999 = 3*5*5*5 = 375
Added to this we can also have 4000
Therefore the number of 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 = 375+1 = 376
Answer is (D)
Hit Kudos if this helped!
Posted from my mobile device
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