Mrs. Torres forgot the PIN of her ATM account, but she knows that the digits she used are 1, 4, 6, and 7. What are the possible PINs of her account? Write them down.
Answers
Answer:
1467, 4671, 6714, 7146, 7641, 6417, 4176, 1764, 1647, 1674, 1746, 1764,etc
The possible PINs of her account are 1467, 1476, 1647, 1674, 1746, 1764, 4167, 4176, 4617, 4671, 4716, 4761, 6147, 6174, 6417, 6471, 6714, 6741, 7146, 7164, 7416, 7461, 7614 and 7641.
Step-by-step explanation:
Case 1. When 1 is the first digit
When 1 is the first digit, 4, 6 and 7 can interchange among each other. They form 467, 476, 647, 674, 746 and 764.
So, the four digit PINs are 1467, 1476, 1647, 1674, 1746 and 1764.
Case 2. When 4 is the first digit
When 4 is the first digit, 1, 6 and 7 can interchange among each other. They form 167, 176, 617, 671, 716 and 761.
So, the four digit PINs are 4167, 4176, 4617, 4671, 4716 and 4761.
Case 3. When 6 is the first digit
When 6 is the first digit, 1, 4 and 7 can interchange among each other. They form 147, 174, 417, 471, 714 and 741.
So, the four digit PINs are 6147, 6174, 6417, 6471, 6714 and 6741.
Case 4. When 7 is the first digit
When 7 is the first digit, 1, 4 and 6 can interchange among each other. They form 146, 164, 416, 461, 614 and 641.
So, the four digit PINs are 7146, 7164, 7416, 7461, 7614 and 7641.
Finally we have twenty four PINs: 1467, 1476, 1647, 1674, 1746, 1764, 4167, 4176, 4617, 4671, 4716, 4761, 6147, 6174, 6417, 6471, 6714, 6741, 7146, 7164, 7416, 7461, 7614 and 7641.
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