I believe the following reflects the intent of the problem:
There are four letters A, B, C, and D that have to go into 4 envelopes addressed to a, b, c, and d respectively. In how many ways can the four letters be put in the 4 envelopes such that every letter goes into a wrong envelope?
A. 20
B. 12
C. 9
D. 6
E. 4
Let the correct ordering be ABCD.
Strategy:
Write out the possible arrangements for ONE CASE.
Use this information to determine the number of possible arrangements for the REMAINING CASES.
Case 1: A in the second position
The following arrangements are viable:
BADC
CADB
DABC
Total options = 3.
Implication:
When A is in the 3rd position, there will be 3 more options.
When A is in the 4th position, there will be 3 more options.
Total options = 3+3+3 = 9.
The correct answer is
C.
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