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How many two-digit numbers can be formed using digits (1, 2, 3, 4, 5,
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10 Aug 2023, 08:13
10 Aug 2023, 08:13
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Question Stats:
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How many two-digit numbers can be formed using digits (1, 2, 3, 4, 5, 6) such that units place is greater than the tens place?
A. 10
B. 12
C. 15
D. 18
E. 20
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A. 10
B. 12
C. 15
D. 18
E. 20
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Re: How many two-digit numbers can be formed using digits (1, 2, 3, 4, 5,
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13 Aug 2023, 09:13
13 Aug 2023, 09:13
Dear Sir,
can you please recheck the OA? we can select 2 digits out of 6 digits in 30 ways and exactly half of those 30 will have unit digit greater than tens digit.
alternatively, if we brute force, then the numbers are: 12, 13, 14, 15, 16, 23, 24, 25, 26, 34, 35, 36, 45, 46, 56. So, IMO, answer should be C
can you please recheck the OA? we can select 2 digits out of 6 digits in 30 ways and exactly half of those 30 will have unit digit greater than tens digit.
alternatively, if we brute force, then the numbers are: 12, 13, 14, 15, 16, 23, 24, 25, 26, 34, 35, 36, 45, 46, 56. So, IMO, answer should be C
How many two-digit numbers can be formed using digits (1, 2, 3, 4, 5,
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13 Aug 2023, 13:28
13 Aug 2023, 13:28
Expert Reply
OE
We have to form all the two-digit numbers which can be formed using the digits 1, 2, 3,
4, 5, 6 such that the units place is greater than the tens place.
Now, as we have to keep the units place greater than the tens place, so it means we
cannot repeat the numbers.
And, whenever we select two numbers, they can only be placed in 1 way as the units’
place has to be greater than the tens place.
So, their arrangement can only be done in one way.
Now, Number of ways to select two numbers out of the given 6 numbers = 6C2
And the number of ways to arrange them such that the units place is greater than the
tens place = 1
Hence, the total number of two-digit numbers which can be formed using the digits 1, 2,
3, 4, 5, 6 such that the units place is greater than the tens place = 6C2 × 1 = 15
Ans. (B)
The correct answer is C
We have to form all the two-digit numbers which can be formed using the digits 1, 2, 3,
4, 5, 6 such that the units place is greater than the tens place.
Now, as we have to keep the units place greater than the tens place, so it means we
cannot repeat the numbers.
And, whenever we select two numbers, they can only be placed in 1 way as the units’
place has to be greater than the tens place.
So, their arrangement can only be done in one way.
Now, Number of ways to select two numbers out of the given 6 numbers = 6C2
And the number of ways to arrange them such that the units place is greater than the
tens place = 1
Hence, the total number of two-digit numbers which can be formed using the digits 1, 2,
3, 4, 5, 6 such that the units place is greater than the tens place = 6C2 × 1 = 15
The correct answer is C
