3 digit numbers with 0 - 5

wilderness · Posted: Wed Jul 23, 2008 9:40 am Post subject: 3 digit numbers with 0 - 5

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?

Was able to calculate that there will be total 100 numbers who satisfy this criteria.

6 P 3 - 5 P 2 = 100

But how to count the odd and even. Would they be fifty - fifty.

I found the explanation below but it makes no sense because the same logic can be used to calculate that the even numbers are also 48 !

Odd: fix last as odd, 3 ways __ __ 3
now, left are 5, but again leaving 0, 4 for 1st digit & again 4 for 2nd digit: 4 4 3 =48 Odd.

sudhir3127 · Posted: Wed Jul 23, 2008 10:04 am Post subject:

100 what u got is right ... but according to me number of odds are 48 and even are 52,

here it goes..
last digit to be odd can be (1 3 5) 3 ways
first digit can be in 4 ways second digit can also be in 4 ways
hence 4*4*3 = 48 ways..

for even

consider last two digits can be 2,4 hence 2 ways..

first digit can be in 4 ways second digit can also be in 4 ways
hence 4*4*2 = 32 ways.

consider zero as its a special case ..

last digit is 0 hence 1 way

first digit can be in 5 ways second digit can also be in 4 ways

hence 5*4*1 = 20 ways

hence number of odds = 48
number of even = 32+20 = 52

total 100..

hope it clear...

egybs · Posted: Wed Jul 23, 2008 10:04 am Post subject:

Without thinking about it too much you know that there should be a few more evens than odds... It isn't 50/50 because you can't have 0 be the first number... Since you can't have it as the first digit, it becomes slightly more likely for it to be either the second or third digit than any of the other digits. And obviously when 0 is the last digit, the number is even.. so there's going to be a larger number of even numbers than odd numbers. depending on the answer choices... this could be enough to pick the correct answer.

For any non-0 number, the odds that it appears in the 3rd digit is going to be 4/5*4/5*1/4 = 4/25 = 16/100

For 0, it will be: 4/5*1/4 = 1/5 = 5/25 = 20/100

So let's add up all the possible evens:

20/100 + 16/100 + 16/100 (odds of zero, 2 or 4)

and we get 52/100

evansbd · Posted: Wed Jul 23, 2008 10:33 am Post subject: Explanation

Can someone explain 5P2?

sudhir3127 · Posted: Wed Jul 23, 2008 10:40 am Post subject:

3 digit number out of 0 1 2 3 4 5
u cant place zero in first place hence u have 5 options
second place u have 5 options as well
third place in 4 ways

hence 5*5*4 = 100 ways

hope it is clear