Question

How many three-digit numbers can be written using digits from the set {2, 3,4, 5, 6} without repeating digits?

Answer 1

Answer:

I think you mean ‘repetition’ of digits is not allowed when you say ‘terrain' of digits is not allowed. If it is so, I will proceed further.

Three digit numbers have Hundreds place, Tens place and Units place. There are six digits, 1,2,3,4,5 and 6 are available. The Hundreds place can be filled up by any one of these 6 digits and can therefore be filled up in 6 ways. Since repetition of digits is not allowed we are left with 5 digits to fill up the Tens place. So Tens place can be filled up in 5 ways. Using the same argument we can fill up the Units digit in 4 ways. Hence we can form (6)(5)(4) = 120 numbers of three digits using the digits 1,2,3,4,5,6 without repetition.

Step-by-step explanation: