Pc-3digit number

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

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

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.

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.

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.

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

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 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

very nice question advita, and equally good explanation Anshu

excellent, thanks Anshu

kudos anshu!!

Thanks for the "thanks" guys !