Problem Solving

How many 4-digit numbers are such that they include the digit '3' exactly twice?

[quote="sanju09"]How many 4-digit numbers are such that they include the digit '3' exactly twice?[/quote]

Can you have the number that starts with 0xxx or 0033 as a 4-digit number?
If 0 can be used, multiply (10 * 10 * 1 * 1) * 4!/2!2! = 600

Can you have the number that starts with 0xxx or 0033 as a 4-digit number?
If 0 can be used, multiply (10 * 10 * 1 * 1) * 4!/2!2! = 600

I think we are going to give GMAT and get into prestigious B-Schools, and does this suits us to say 0033 or 33 is a 4 digit number??:P
If you cannot answer a question I would advice better not to make a mockery of yourself

by the way here is the solution:

4-digit no = ABCD

A position can have numbers from 1 to 9 and not 0

so A can be filled in 9 ways

But B can have all the numbers,

so B can be filled in 10 ways

And C and D can only have 3 as number,so only 1 way

No.of ways = 9*10

But BCD can arrange among themselves in 3!/2! = 3

Total No. of ways = 9*10*3 =270


Hope the answer is now clear.

Well I'm really happy to know that you got a good laugh from this. Seeing that it was my first post, you really made my experience on this forum warm and welcoming. I do appreciate your motivational words that really inspire me to keep trying even when I don't know the answer and decide to take a guess. Its nice to know that there are strangers on the other side of the computer who do not judge another's learning skills and abilities. Thanks. I'll try to stop creating a mockery of myself now by being a pompous jerk like some others on this forum.

@quriousaddict

Well if in any way I sound rude to you, then I really apologize for that.
You are replies and attempt to solve the questions will be very much welcome to this forum like others.

But,

Can you have the number that starts with 0xxx or 0033 as a 4-digit number?

I won't support you on this at least.Being new to the forum is an alibi for your silly mistake.

You can ask a 6 year old neighborhood kid about the question you posted,may be he has a better answer to it!!

Being new to the forum does not mean you lack common sense, don't you think?

We are all humans and by nature we commit mistakes. I would advice you to approach every question you face in a logical way without assuming anything from your side(trust me assuming anything from your side is really fatal in Verbal part!!)
I would appreciate to see more answers from you in the future.
In case of any advice don't hesitate to pm me.

Cheers,

Karan

It might not be the case but you really sounded loutish in your reflexes here, which in any case not going to pay any dividends to either side, gmat740! We can afford to be genteel if anybody slips here; can't we?

Out of the 4-digit numbers formed with repetition we need to find how many of them have exactly two 3s. There are two cases, first one first, when one of the 3s is in the first place, if we fix the first place with 3, then the remaining three places can be filled in 9*9*3 = 243 ways ("why?/how?" is for the readers to bother). The second case would be when none of the 3s is in the first place, this would lead the total number of arrangements to be equal to 8*9*3 = 216 ways ("why?/how?" is again for the readers to bother). Total such numbers will be 243 + 216 = 459.

We are here to learn from each other and not judge or make fun of each other. So please do not make comments that can be deemed offensive.

Regards

That really was a simple mistake. If you are thinking 4 digit numbers such as on a lock, then 0033 would be legit.

I know he asked for a number, but the mistake really isn't hard to make

Hello Everyone,

To my best knowledge I am definitely not the best person to judge anyone's quality and I believe our GMAT score will reflect our ability in a proper way

As far as my comments are concerned, I think my comments have been misinterpreted, or may be my way of presenting them was not correct.Whichever way it is, I sincerely apologize if it hurts anybody's sentiments.

They were meant to point out the mistake so that one can learn from them. But it looks like my comments have taken a wrong turn!!

As my test date is very near Some mistakes which I find very silly might not be actually silly for others.


Regards,

Karan

Thanks for clearing that up. Best of luck with your test .

This is waay off topic but... GMAT740 I like your avatar. did you design it yourself?

This is waay off topic but... GMAT740 I like your avatar. did you design it yourself?

I don't know if this is a complement or something else but anyways...

Well the avatar is inspired by what my girl-friend calls me "Joker" because I behave silly when she is around.

gmat740 wrote:

This is waay off topic but... GMAT740 I like your avatar. did you design it yourself?

I don't know if this is a complement or something else but anyways...

Well the avatar is inspired by what my girl-friend calls me "Joker" because I behave silly when she is around.

So, only your girl friend calls you Joker

This is going way too outside the topic of discussion!

Well my purpose of being here at this forum is to learn and to help others learn. So any of you want to communicate with me on any non-educational issues, contact me on other networks, like facebook.
If I feel like answering your personal queries, I would definitely do that.


Thank You

I'm counting 459 numbers too.

I see 4C2 or 6 possible combinations that we need to address.

1. 33XX
2. 3X3X
3. 3XX3
4. X33X
5. X3X3
6. XX33

Looking at the number of possibilities for each combination:
1. 1 x 1 x 9 x 9 = 81
2. 1 x 9 x 1 x 9 = 81
3. 1 x 9 x 9 x 1 = 81
4. 8 x 1 x 1 x 9 = 72
5. 8 x 1 x 9 x 1 = 72
6. 8 x 9 x 1 x 1 = 72

4, 5, and 6 all have 8 ways for the first digit since 0 and 3 are invalid values.

Add all the possibilities together and you get 459.