How many 3-digit passcodes are possible if digits, chosen from the set {1,2,3,4,5,6,7} if numbers cannot be repeated and the first digit must be an odd number?

Answer 1

Hi Megan,

The answer is 120. Here's how I solved it:

You have to create a 3-digit passcode, like so: _ _ _

Now, the first digit has to be an odd number. There are 4 odd digits: 1,3,5, and 7.

So there are 4 choices for the first digit: 4 _ _

The next digit can be any of the digits EXCEPT it can't be the same as the one you just selected. So there are 7 - 1 = 6 digits that can be placed into the second position: 4 6 _

Finally, the last digit. Since you can't repeat a digit, the last place can be any digit you didn't pick in the first two positions, so there are 7 - 2 = 5 digits available: 4 6 5. We multiply these together to get 4*6*5 = 120 possible combinations.

Hope this helped!