Pc-3digit number

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Thu Jan 13, 2011 1:04 am

How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Thu Jan 13, 2011 1:14 am

advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.

the hundredth digit can be placed in 5 ways, the ten's digit is placed in five ways, the unit's digit is placed in four ways

5*5*4=100 numbers with different digits can be formed from 0,1,2,3,4,5

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towerSpider: Master | Next Rank: 500 Posts; Posts: 155; Joined: Mon Dec 13, 2010 11:02 am; Thanked: 3 times

by towerSpider » Thu Jan 13, 2011 1:23 am

advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.

First of all, this is not a GMAT question. You have asked for three answers from one question.

Total numbers: 5*5*4

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Thu Jan 13, 2011 1:42 am

advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.

we are given consecutive row of odd-even numbers, hence 50% of numbers are even, 50% are odd or 50 numbers are even the remaining 50 numbers are odd.

hope this helps.

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Thu Jan 13, 2011 1:47 am

thanks guys...but i think this is gmat question...!!

i could solve the total=100 such numbers...but what about odd/or even numbers.

if we get odd... then off course even= 100-odd.

(so, basically this is not asking three answers..but if Q asks- how many 3 digit odd numbers are possible. then it is quite GMAT like Q)

..so pl could you explain other part of Q.
thanks once again.

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Thu Jan 13, 2011 5:09 am

advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.

How many 3 digit numbers can be formed :

Hundred digit -> 5 ways (you can't put 0)
Tens digit -> 5 ways (all but what we put at hundred's place)
Unit digit -> 4 ways (all but what we put at hundred and unit place)

So, total no. of ways = 5*5*4 = 100

How many odd 3 digit numbers can be formed :
Unit digit -> 3 ways (1,3,5)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)

So, total no. of ways = 3*4*4 = 48

How many even 3 digit numbers can be formed :

Even numbers = Total - odd numbers = 100 - 48 = 52

OR (Go through this just for learning)
Two cases:

(unit digit is 2 or 4):
Unit digit -> 2 ways (2,4)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 4*4*2 = 32

(unit digit is 0):
Unit digit -> 1 way (0)
Hundred digit -> 5 ways (as 0 is already selected, choose anything)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 1*5*4 = 20
Total No. of ways = 32+20 = 52

Note : You can't say that there will be 50% of even numbers and 50% of odd numbers, as because of 0, it is not symmetric. If it would have been any other distinct even number in place of 0, then you can take 50% even and 50% odd numbers. 0 adds a restriction for the hundred's place which other digit don't. So in this case, number of odd numbers are at disadvantage hence would be less than no. of even numbers.

Last edited by anshumishra on Thu Jan 13, 2011 5:45 am, edited 2 times in total.

Thanks
Anshu

(Every mistake is a lesson learned )

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Thu Jan 13, 2011 5:15 am

thanks guys...thanks anshu...very nice &clear explanation...
your answers are absolutely correct.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Thu Jan 13, 2011 6:18 am

anshumishra wrote:
advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.
How many odd 3 digit numbers can be formed :
Unit digit -> 3 ways (1,3,5)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)

So, total no. of ways = 3*4*4 = 48

Hi Anshu, though I looked other forums, still am not convinced about 50/50 rule - we may get 48 even with unit digit -> 3 ways (0,2,4)
...
total 3*4*4=48

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Thu Jan 13, 2011 7:09 am

Night reader wrote:
anshumishra wrote:
advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?

pl explain.
How many odd 3 digit numbers can be formed :
Unit digit -> 3 ways (1,3,5)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)

So, total no. of ways = 3*4*4 = 48

Hi Anshu, though I looked other forums, still am not convinced about 50/50 rule - we may get 48 even with unit digit -> 3 ways (0,2,4)
...
total 3*4*4=48

Night reader , please check out the "note" section in my previous post. Use any other even no. in place of 0 then you can apply the 50-50 rule.

Here, we can't use : 3*4*4 (because depending on whether you have selected 0 or (2 and 4), the hundred digit can be selected in 5 ways or 4 ways respectively).

That is why, I have subdivided them into two cases : (copy/paste) from previous post :-

Two cases:

(unit digit is 2 or 4):
Unit digit -> 2 ways (2,4)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 4*4*2 = 32

(unit digit is 0):
Unit digit -> 1 way (0)
Hundred digit -> 5 ways (as 0 is already selected, choose anything)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 1*5*4 = 20
Total No. of ways = 32+20 = 52

Thanks
Anshu

(Every mistake is a lesson learned )

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Thu Jan 13, 2011 7:34 am

very nice question advita, and equally good explanation Anshu

Cheers !!

Quant 47-Striving for 50
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https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Thu Jan 13, 2011 7:58 am

excellent, thanks Anshu

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Fri Jan 14, 2011 4:32 am

kudos anshu!!

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Jan 14, 2011 4:34 am

Thanks for the "thanks" guys !

Thanks
Anshu

(Every mistake is a lesson learned )

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