Question 1197328: Four people form a line at a grocery store. What is the probability that they line up in descending order of age?
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849)   (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
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Answer: 1/24
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Explanation:
There are 4 people for the first slot, then 3 for the next, and so on until we count down to 1
4,3,2,1
Multiply out those items
4*3*2*1 = 24
Many calculators have an exclamation mark button, which represents factorials
4! = 4*3*2*1 = 24
4! = 24
This represents the number of ways to line up the four people. Order matters of course.
Only one way has all four people in the correct order of descending age.
Therefore, we arrive at 1/24 as our answer.
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An alternative way to calculate the '24' is to follow these steps, through use of the nPr permutation formula.
n P r = (n!)/( (n-r)! )
4 P 4 = (4!)/( (4-4)! )
4 P 4 = (4!)/( 0! )
4 P 4 = (4*3*2*1)/( 1 )
4 P 4 = 4*3*2*1
4 P 4 = 24
Though as you can probably spot, the factorial of 4! = 4*3*2*1 is part of 4P4. Meaning that we're basically following the same pathway as the previous section.
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