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If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man
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Updated on: 07 Jul 2022, 13:46
Updated on: 07 Jul 2022, 13:46
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Question Stats:
20% (02:42) correct
80% (01:15) wrong based on 5 sessions
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If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how many different even numbers are possible?
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Part of the project: Skill Builder Project for a Q170
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man
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07 Jul 2022, 12:00
07 Jul 2022, 12:00
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arjunbhat04 wrote:
In the qn,it is not mentioned that number repetition is allowed or not so:
with repetition:
thousandth place can be filled in 4 ways as 0 is not possible
hundredth place can be filled in 5 ways
tenth place can be filled in 5 ways
unit place can be filled in 3 ways(0,2,4) == 4*5*5*3 ->300 ways
without repetition:
thousandth place can be filled in 4 ways as 0 is not possible
unit place can be filled in 3 ways(0,2,4)
hundredth place can be filled in 3 ways
tenth place can be filled in 2 ways
== 4*3*2*3 ->72 ways
Is this correct?
with repetition:
thousandth place can be filled in 4 ways as 0 is not possible
hundredth place can be filled in 5 ways
tenth place can be filled in 5 ways
unit place can be filled in 3 ways(0,2,4) == 4*5*5*3 ->300 ways
without repetition:
thousandth place can be filled in 4 ways as 0 is not possible
unit place can be filled in 3 ways(0,2,4)
hundredth place can be filled in 3 ways
tenth place can be filled in 2 ways
== 4*3*2*3 ->72 ways
Is this correct?
Judging from the official answer, it looks like the question was intended to have no repetition.
The problem with your solution here is that, if the first (thousands) digit is 4 or 2, then there aren't 3 ways in which the units digit can be chosen.
I would probably break the solution into two cases:
case 1: the units digit is 2 or 4.
Here, there are 2 options for the units digit.
There are 3 options for the thousands digit (anything but 0 or the even digit chosen for the units digit)
There are 3 remaining options for hundreds digit
And 2 remaining options for tens digit
Total = 2 x 3 x 3 x 2 = 36
case 2: the units digit is 0.
Here, there 1 option for the units digit.
There are 4 options for the thousands digit (anything but 0)
There are 3 remaining options for hundreds digit
And 2 remaining options for tens digit
Total = 1 x 4 x 3 x 2 = 24
Answer = 36 + 24 = 60
General Discussion
Re: If 0, 1, 2, 3, and 4 are arranged to form a four-digit number, how man
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19 Apr 2022, 11:45
19 Apr 2022, 11:45
Thanks for the question Carcass, will wait for OE
