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# How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6

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Intern
Joined: 03 Nov 2019
Posts: 43
How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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26 Nov 2019, 11:14
5
00:00

Difficulty:

75% (hard)

Question Stats:

35% (01:50) correct 65% (02:13) wrong based on 31 sessions

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How many even numbers of 4 digits can be formed using digits 0,1,2,3,4,5 & 6?
Repetition is not allowed.
A) 480
B) 420
C) 864
D) 840
E) 828
Intern
Joined: 23 Sep 2017
Posts: 3
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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26 Nov 2019, 11:30
1
The correct answer choice is C as 6*6*6*4.

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VP
Joined: 19 Oct 2018
Posts: 1174
Location: India
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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26 Nov 2019, 11:47
Case 1- Unit digit is 2, 4 or 6

Total possible numbers= 5*5*4*3=300

Case 2- unit digit is 0

Total possible numbers- 6*5*4*1=120

Number of even numbers of 4 digits can be formed using digits 0,1,2,3,4,5 & 6= 300+120=420

Ansh777 wrote:
How many even numbers of 4 digits can be formed using digits 0,1,2,3,4,5 & 6?
Repetition is not allowed.
A) 480
B) 420
C) 864
D) 840
E) 828
Director
Joined: 18 Dec 2017
Posts: 862
Location: United States (KS)
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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26 Nov 2019, 11:57
1
We have to consider cases because we are dealing with zero.

Case 1- Say unit digit is 0.
We have to form a 4 digit number and we have 7 choices out of which 0 is gone.
So we can do 6*5*4*1= 120

Case 2- Unit digit can be 2,4,6.
We have to form a 4 digit number and we have 7 choices out of which 3 choices are gone.
So we can do 5*5*4*3=300 (Left most digit cannot be 0 but the next digit can be non zero.

Total=120+300= 420
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Intern
Joined: 25 Nov 2019
Posts: 17
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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26 Nov 2019, 13:18
My answer is missing what did I do wrong
1000's can't start with a zero so there are (6) choices 100's is n-1 but we get 0 back so (6) 10' is N-2 or (5) and evens are (4)

if i'm guessing my answer includes too many due to the no repeats on evens but my answer should be 720
Intern
Joined: 03 Nov 2019
Posts: 43
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6  [#permalink]

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03 Dec 2019, 09:27
Stonely wrote:
My answer is missing what did I do wrong
1000's can't start with a zero so there are (6) choices 100's is n-1 but we get 0 back so (6) 10' is N-2 or (5) and evens are (4)

if i'm guessing my answer includes too many due to the no repeats on evens but my answer should be 720

What if out of 4 even
You accidentally placed any one of them except 0 at 1000's place already then there won't be 4 option for units place rather it would be 3
or one at 1000's (except 0) one at 100's place then there would be 2 options for unit place.
or one at 1000's (except 0) one at 100's place and one at 10's place then there would be 1 options (i.e. 0) for unit place.

So we have to pay attention that we place any one out of 4 even at units place first and then remaining numbers at other place, keeping in mind that we exclude all selections where 0 is at 1000's place, else it would be a 3 digit number.

Alternative Method
Units Place- 4 options
Tens place- 6 Options
Hundreds place- 5 Options
Thousands place- 4 Options
Total Ways= 4*5*6*4 = 480 ways..............A
Now we remove all the arrangements in which 0 might have skipped from unit, tens and hundreds place and placed at Thousands place
(i.e. only one option 0 at Thousands, any one even number out of 3 at units place and remaining numbers at hundreds and tens)
=1*5*4*3=60 ways .................B
Therefore
Total Even 4 digit Numbers that could be formed = A-B = 480-60 = 420 ways.
Re: How many even numbers of 4 digit can be formed through 0,1,2,3,4,5 & 6   [#permalink] 03 Dec 2019, 09:27
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