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Bunuel
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How many 5 digit numbers have all digits odd and have exactly one of 11 Jan 2022, 03:00
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E
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35% (medium)

Question Stats:

71% (01:56) correct 29% (02:09) wrong based on 217 sessions

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How many 5 digit numbers have all digits odd and have exactly one of their digits as 5?

(A) 600
(B) 720
(C) 960
(D) 1,024
(E) 1,280
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E
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kritid99
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How many 5 digit numbers have all digits odd and have exactly one of 18 Jan 2022, 23:41
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From 1-10, there are 5 odd numbers. According to the question, there has to be 5 in the required number. This leaves 4 odd numbers.
Since repetitions are allowed and 5 can take 5 different positions, the no. of ways in which such a number be constructed is thus given by (4*4*4*4*1)*5 = 1280

Hence, IMO the answer is E.
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How many 5 digit numbers have all digits odd and have exactly one of 26 Jun 2026, 12:27
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Though Repetititions are allowed, shouldn't it be more like (5*5*5*5*1)*5?

kritid99
From 1-10, there are 5 odd numbers. According to the question, there has to be 5 in the required number. This leaves 4 odd numbers.
Since repetitions are allowed and 5 can take 5 different positions, the no. of ways in which such a number be constructed is thus given by (4*4*4*4*1)*5 = 1280

Hence, IMO the answer is E.
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Bunuel
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How many 5 digit numbers have all digits odd and have exactly one of 26 Jun 2026, 12:37
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How many 5 digit numbers have all digits odd and have exactly one of their digits as 5?

(A) 600
(B) 720
(C) 960
(D) 1,024
(E) 1,280

Odd digits are:

1, 3, 5, 7, 9

Exactly one digit must be 5.

Choose the position of 5: 5 choices

Each of the other 4 positions can be one of:

1, 3, 7, 9

So each has 4 choices.

Total:

5 * 4^4 = 1,280

Answer: E.

jatb
Though Repetititions are allowed, shouldn't it be more like (5*5*5*5*1)*5?
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No. That would allow more than one 5.

Once we choose the position of the single 5, the other four digits can be odd, but cannot be 5.

So each of the other four positions has only 4 choices: 1, 3, 7, 9.

Thus:

5 * 4 * 4 * 4 * 4 = 1,280

“Repetition allowed” means digits like 1, 1, 1, 1 can repeat, it does not allow another 5, because the question says exactly one 5.
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