Watch Wise!
Probability
Level
4
Suppose, you are a mathematician.You went to watch a car race which you are very fond of.It was Quarter-final and race consisted of only 5 cool and different cars.In how many ways can 5 cars cross the finish line.
(ties are possible for any number of cars).
The answer is 541.
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a) 5 cars tie - 1 way
b) 4 cars tie - 5C4 * 2! = 10 ways
c) 3 cars tie - 5C3 * 3! = 60 ways
d) 3 cars tie and a pair ties - 5C3 * 2! = 20 ways
e) 2 cars tie - 5C2 * 4! = 240 ways
f) 2 pairs of cars tie-- You can select a pair in 5C2 ways then select another pair in 3C2 ways so10*3 = 30 but there will be repeats so half that will be 15 * 3! = 90 ways
g) no cars tie -- 5! = 120 ways.
total of 541 ways