SAT – Counting and Ordering

Q: Four people are to stand side by side for a photo. The shortest two people must stand at the ends, while the tallest two people must stand in the center. How many ways are there to arrange the people for the photo?
Answer: 4
Explanation: Use the Counting Principle.  Set up four blanks:
___  ___  ___  ___ to represent the four positions.
Decide on the number of possibilites for each position.
The first position has 2 possibilities (the 2 shortest people):
_2_  ___  ___  ___.  Whichever of the two shortest people isn’t in the first spot, will have to be in the fourth spot:
_2_  ___  ___  _1_.
Do the same for the middle two positions, using the two tallest people:
_2_  _2_  _1_  _1_.  Now, multiply these numbers together: 4.
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