How many four-digit numbers can be formed using 0 1 2 and 5?

Answer 1

This one's a little tricky. Numbers can't start with zero, so "0323" is not really a 4-digit number (although you could use it as a Personal Identification Number for your ATM card). So, there are really only three digits that can be in the most significant place (the thousands place, in this case). Therefore, there are 3 x 4 x 4 x 4 = 192 unique 4-digit numbers that can be formed. Note that that amount allows for repetition of digits. If you are not allowed to repeat digits (the question placed no such restriction), then there are only 3 x 3 x 2 x 1 = 18 different numbers. By the way, this problem explores permutations, where the order of the elements matters. When the order doesn't matter, it's a combination. For example, if 123 and 321 are considered unique elements, then you are doing permutations. If they are considered the same element, you are doing combinations. Calculating the number of combinations is a bit trickier.