Determine whether the statement is true or false.

The number of four-digit numbers that can be formed from the digits 1, 2, 3, and 4 if the number must be even is 179.

Question

Determine whether the statement is true or false.
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The number of four-digit numbers that can be formed from the digits 1, 2, 3, and 4 if the number must be even is 179.

Quizplus · Accepted Answer

To form an even number, the units digit must be 2 or 4. 
Case 1: Units digit is 2 
Number of choices for units digit = 1 
Number of choices for thousands digit = 3 (cannot be 1) 
Number of choices for hundreds digit = 2 (cannot be 2 or 4) 
Number of choices for tens digit = 1 (must be 4) 
Total number of choices = 1 × 3 × 2 × 1 = 6 
Case 2: Units digit is 4 
Number of choices for units digit = 1 
Number of choices for thousands digit = 3 (cannot be 1) 
Number of choices for hundreds digit = 2 (cannot be 2 or 4) 
Number of choices for tens digit = 1 (must be 2) 
Total number of choices = 1 × 3 × 2 × 1 = 6 
Total number of four-digit even numbers = 6 + 6 = 12. Therefore, the statement is false.

Determine Whether the Statement Is True or False