# Probability Question: Generate thirty 3-digit numbers,what's the probability for such cases- three different digits,two same digits or three same digits?

A 3-digit number may consist of threee different digits,two same digits or three same digits.Perform a simple experiment to generate thirty 3-digit numbers and tabulate your results.Hence,give a reasonable probability for each of the cases.

What can you deduce?
Math question asked Jun 25, 2013 in Other

So firstly lets see how many numbers can be made out of a 3 digit numbers...
and that is = 9*10*10=900
because the first digit cannot be zero so we will reduce the zero from the ten digits.
and the second case for the number to be having three same digits:
if they have three same digits there will be 9 such 3-digit numbers(you know them all).
if they have 2 of the same digits(inclusive of the 3 same digits number and we will remove them)
then there will be 270 such numbers
{111,112,113......
221,222,223,...
............
991......999}
now after removving those 3 same digit numbers we now have (270-9) i.e.261 numbers
now for the different digits we have 900-9-261=630
now the main part
for the thirty generated number's probablilty will all be a numbers with three different digits we have :
630C30/900C30
and for the numbers to be having 2 digits similar we have
261C30/900C30
Math question answered Jun 27, 2013 by Anon