Answer:
1/154440
Step-by-step explanation:
To calculate the probability it would be the quotient between 1 and the number of ways to choose 5 out of 13, but in this case the order matters, so it would be the permutation 13P5, therefore:
We know that:
nPr = n! / (n-r)!
we replace and we have:
13P5 = 13! / (13-5)! = 154440
The probability that the rack ends up in alphabetical order is 1/154440
The probability that the rack ends up in alphabetical order is 1/154440
This is a question relating to permutation and combination. In order to calculate the probability, it would be the permutation 13P5, and this will be:
nPr = n! / (n-r)!
13P5 = 13! / (13-5)!
= 13! / 8!
= 13 × 12 × 11 × 10 × 9
= 154440
Therefore, the probability that the rack ends up in alphabetical order is 1/154440.
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