The probability that the cd rack ends up in alphabetical order is = 1/240,240.
Based on the given conditions,
Relating to permutation and combination. In order to calculate the probability, it would be the permutation 114P5, and this will be:
nPr represents n permutation r which is calculated as n!/(n-k)!. Permutation refers to the process of arranging all the members of a given set to form a sequence. The number of permutations on a set of n elements is given by n!
The npr formula is used to find the number of ways in which r different things can be selected and arranged out of n different things. This is also known as the permutations formula. The nPr formula is, P(n, r) = n! / (n−r)!.
So,
We can write,
nPr = n! / (n-r)!
Where,
n = 14
r = 5
14P5 = 14! / (14-5)!
14P5 = 14! / 9!
14P5 = 14 x 13 × 12 × 11 × 10 × 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1/9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
We can cancel the coefficients,
14P5 = 14 x 13 × 12 × 11 × 10
14P5 = 240,240
Therefore,
The probability that the cd rack ends up in alphabetical order is = 1/240,240.
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