If a license plate has four different digits on it, what is the probability that the...

If a license plate has four different digits on it, what is the probability that the numbers on the plate will not be in either consecutive increasing or consecutive decreasing order? Show you work.

Expert Solution

Solution:

total number of numbers = 10

number of different license plates formed by four different numbers = ¹⁰C₄ = 5040

number of plates will be in either consecutive increasing or consecutive decreasing order = 14

they are :

(0,1,2,3),(1,2,3,4),(2,3,4,5),(3,4,5,6),(4,5,6,7),(5,6,7,8),(6,7,8,9),(9,8,7,6),(8,7,6,5),(7,6,5,4),(6,5,4,3),(5,4,3,2)(4,3,2,1),(3,2,1,0)

number of plates will not be in either consecutive increasing or consecutive decreasing order = 5040 - 14 = 5026

probability that the numbers on the plate will not be in either consecutive increasing or consecutive decreasing order = 5026 / 5040 = 0.9972

orchestra answered 2 years ago

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