How many ways can a set of 3 not necessarily distinct numbers be chosen from the set of integers from 0 to 9? Two such sets are 5,2,4 and 0,0,7, but 2,4,5 is considered the same as 5,2,4
There should be: [10 +3 - 1] C 3 =12C3 = 220 ways
P.S. If you wanted a list of them, we can give you one.
Here is how guest got that answer :
If all the digits are differerent we have C(10,3) = 120 sets
If two digits are the same and the other is different, we hve 10 ways to pick the two digits and 9 ways to select the remaining one = 10 * 9 = 90 sets
If all 3 digits are the same, we have 10 sets
120 + 90 + 10 = 220 sets (ways)