We have the digits {1,2,⋯,9}. If the digits are randomly arranged in a row, find the...

Question

Question

We have the digits {1,2,⋯,9}.

If the digits are randomly arranged in a row, find the probability that the even numbers occur consecutively (i.e. side by side).

math Statistics-And-Probability

Answer 1

Answer #1

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2, 4, 6, 8 are even numbers. So 4 numbers out of 9 are even numbers. Let these even number be 1 group, as they should together/consecutive.

So 4 odd numbers + 1 even group= 5

These can be arranged in 5! Ways. Within the even numbers, those 4 even numbers can be arranged in 4! Ways.

Hence, 5!4! ways you can arrange such that even numbers are consecutive. This is 120*24 = 2880 ways.

Answer: 2880 ways.

Answer 2

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