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How many four-digit numbers have at least one digit repeating?

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Bunuel
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How many four-digit numbers have at least one digit repeating? [#permalink] New post   02 Nov 2021, 06:15
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A
B
C
D
E

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69% (02:00) correct 31% (02:31) wrong based on 54 sessions
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How many four-digit numbers have at least one digit repeating?

A. 3000
B. 4464
C. 4500
D. 4536
E. 5000
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B
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chetan2u
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Re: How many four-digit numbers have at least one digit repeating? [#permalink] New post   02 Nov 2021, 06:27
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Bunuel wrote:
How many four-digit numbers have at least one digit repeating?

A. 3000
B. 4464
C. 4500
D. 4536
E. 5000



Let the numbers be of type ABCD

No restrictions:
A can take any of 9 digits except 0 => 9 ways
Remaining B, C and D can take any 10 digits as its value => 10 each
Total ways = 9*10*10*10 = 9000

opposite restriction - no digits repeating:
A can take any of 9 digits, except 0 => 9 ways
B can take any of remaining 9 digits including 0 => 9 ways
C can take any of remaining 8 digits including 0 => 8 ways
D can take any of remaining 7 digits including 0 => 7 ways
Total ways = 9*9*8*7 = 4536

Four-digit numbers with at least one digit repeating = 9000-4536 = 4464


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Re: How many four-digit numbers have at least one digit repeating? [#permalink] New post   02 Nov 2021, 07:10
Total 4 digit number combinations = 9 x 10 x 10 x 10 = 9000

Numbers where digits do not repeat = 9 x 9 x 8 x 7 = 4536

Remaining numbers = 9000 - 4536 = 4464

Option B
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Bunuel
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Re: How many four-digit numbers have at least one digit repeating? [#permalink] New post   06 Nov 2021, 18:00
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Bunuel wrote:
How many four-digit numbers have at least one digit repeating?

A. 3000
B. 4464
C. 4500
D. 4536
E. 5000



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Re: How many four-digit numbers have at least one digit repeating? [#permalink]
06 Nov 2021, 18:00
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