How many five-digit codes can be made if the first number cannot be a 0 or a 1 and no numbers can repeat?
+539 There are 8 possibilities for the first, 9 for the second, 8 for the third, 7 for the fourth and 6 for the last. Multiplying we get 24192.
If the first digit cannot be a 0 or 1 then there are 10-2=8 choices for the first digit. The next digit has 10-1=9 digits because we cannot include the number that is the first digit. The third digit thus has 10-2=8 choices, the fourth has 7, and the 5th digit has 6 choices. We multiply this to get 24192 codes.
+934 The first digit has 8 choices, the second digit has 9 choices because you can't repeat digits but you can use 1 or 0 now, the third digit has 8 choice, the fourth digit has 7 choices, and the last digit has 6 choices. So 8*9*8*7*6= 24192 five-digit codes.
Hope it helps!
