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Number of different arrangements of n objects in a row
n!
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Number of different arrangements when objects are repeated
TotalObjects! / (Number!Of!Each!Repeated!)
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Picking groups, where order doesn't matter
(If 3 of 7 standby passengers are selected for a flight, how many diff. combos of standby passengers can be selected?)
Factorial of the total / (Factorial of group 1 * Factorial of group 2)
7! / (3!x4!)
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Permutation where order matters, repetition is allowed
(# of permutations of a 3 digit lock?)
n^r
(3^3, or 3x3x3)
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Order matters, no repetition allowed
(How many different orders of 3 balls selected from 16?)
n! / (n-r)! - choose r things out of n
16! / (16-3)!, or 16! / 13!
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Combination where order DOESN'T matter, repetition is not allowed (like a lottery)
n! / (r![n-r]!)
n is number of things to choose from, you choose r
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Combination where order DOESN'T matter, you can repeat (picking scoops of ice cream)
(n+r-1)! / (r![n-1]!)
n is number of things to choose from, you choose r of them
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Probabilty that X AND Y both occur
Multiply probabilities together
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Probability that independent event X OR event Y will occur
Add probabilities together
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Probability of event X OR event Y, which can occur together
P(X) + P(Y) - P(X+Y)
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