Find the number of three-digit numbers possible if only the digits 0,1,2,3,4 and 5 may be used, the number must be a multiple of 5, and no digit may be used more than twice in the same number.

59 ways

Step-by-step explanation:

We're to consider the digits 0,1,2,3,4,5.

If we're to find three digit number and were given that the number must be a multiple of 5, then the Last number can either be 0 or 5. That is the last number can be chosen in two ways.

Since 0 can not start a number, then, we are left with 5 different ways to pick our first number

If there are no restrictions, then 2nd number can be chosen in 6 different ways.

Total number of ways possible without restrictions = 5*6*2= 60ways.

Going by this method, the only number that can be used more than twice is the number "5" and this can happen in only one way,

Hence, total number of ways to get a three-digit number if no two numbers are repeated = 60 -1 = 59ways.