SOLUTION: In how many ways can 2 pictures, selected from a group of 5 different pictures, be arranged in a row on a wall?

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Question 315397: In how many ways can 2 pictures, selected from a group of 5 different pictures, be arranged in a row on a wall?
Answer by moshiz08(60)   (Show Source): You can put this solution on YOUR website!
There are two positions to fill.
In the first spot, there are five possibilities: A, B, C, D, or E.
In the second spot there are four remaining possibilities (because one has already been selected for the first spot).
If A is the first one, the second one could be one of the remaining four:
AB
AC
AD
AE
If B is the first one, the second one could be one of the remaining four:
BA
BC
BD
BE

If C is the first one, the second one could be one of the remaining four:
CA
CB
CD
CE

If D is the first one, the second one could be one of the remaining four:
DA
DB
DC
DE

If E is the first one, the second one could be one of the remaining four:
EA
EB
EC
ED
Hence there are 20 possibilities.
Actually, you don't even have to list them all out like this. Just recognize the pattern that there are 5 possibilities for the first one, and for each of them there are 4 for the second one (after the first has already been selected). Thus we multiply, 4 * 5 to get 20.
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