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Answers
Answer:
Step 2 of solving this GRE Permutation Question: Find the number of ways the student can leave the classroom through a different door.
The student cannot leave the classroom through the door she entered.
The number of choices to choose a door to leave is down to 4
Step 3 of solving this GRE Permutation Question: Compute the number of possibilities
If the student entered through A, she could leave through B or C or D or E.
There are 4 possibilities of entering through A and leaving through a different door viz., AB, AC, AD, AE.
If the student entered through B, she could leave through A or C or D or E.
There are 4 possibilities of entering through B and leaving through a different door viz., BA, BC, BD, BE.
If the student entered through C, she could leave through A or B or D or E.
There are 4 possibilities of entering through C and leaving through a different door viz., CA, CB, CD, CE.
If the student entered through D, she could leave through A or B or C or E.
There are 4 possibilities of entering through D and leaving through a different door viz., DA, DB, DC, DE.
If the student entered through E, she could leave through A or B or C or D.
There are 4 possibilities of entering through E and leaving through a different door viz., EA, EB, EC, ED.
There are a total of 4 + 4 + 4 + 4 + 4 = 20 ways.
We could also arrive at the same answer by saying - there are 5 ways to enter AND 4 ways to leave.
So, a total of 5 × 4 = 20 ways
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