How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if the numbers mast be even and digits are not repeated? (Hint: Begin with the digit where there is a restriction on the choices.)
A)120
B)60
C)360
D)4,096
E)10

Question

How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if the numbers mast be even and digits are not repeated? (Hint: Begin with the digit where there is a restriction on the choices.) ​
A)120
B)60
C)360
D)4,096
E)10

Quizplus · Accepted Answer

For a number to be even, it must end in an even digit. From the given digits, only 8 is even. So, the last digit is fixed as 8. For the first digit, we have 5 choices (1, 3, 5, 7, or 9), since we can't use 8 again. For the second digit, we have 4 remaining choices (since we've already used one digit for the first position and 8 is fixed for the last), and for the third digit, we have 3 choices. Therefore, the total number of combinations is 5 * 4 * 3 * 1 = 60.

How Many Four-Digit Numbers Can Be Formed from the Digits