Question 1199288: If repeated digits are not allowed, the number of four-digit even numbers that can be formed from the digits 0, 1, 5, 6, 7, 8 and 9 is
a) 120 b) 240 c) 320 d) 360 e) 480
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
Case 1: the last (4th) digit is 0.
Choose the last digit 0. That's 1 way.
Then choose the first digit any of {1,5,6,7,8,9). That's 6 ways.
Then choose the second digit any of the 5 remaining ways. That's 5 ways.
Then choose the third digit any of the 4 remaining ways. That's 4 ways.
Total for case 1: (1)(6)(5)(4) = 120
Case 2: the last (4th) digit is 6 or 8.
Choose the last digit either of {6,8}. That's 2 ways.
Then choose the first digit any of the remaining 5 ways (can't choose 0).
That's 5 ways.
Then choose the second digit any of the 5 remaining ways. (can choose 0),
That's 5 ways.
Then choose the third digit any of the 4 remaining ways. That's 4 ways.
Total for case 2: (2)(5)(5)(4) = 200
Grand total: 120+200 = 320
Edwin
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