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------------------------------------------------ If the letters of the word "Geraniums" are randomly arranged, what is the probability that the arrangement spells the word correctly?

Answer :

The probability that the letters of the word 'Geraniums' are randomly arranged to spell the word correctly is [tex]\frac{1}{362880}[/tex].

To determine the probability that the letters of the word 'Geraniums' are randomly arranged to spell the word correctly, we can follow these steps:

  1. Calculate the total number of possible arrangements of the letters in 'Geraniums'.

The word 'Geraniums' has 9 distinct letters. The total number of arrangements of these letters is given by the factorial of the number of letters, which can be expressed as:

[tex]9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362880[/tex]

  1. Identify the number of favorable outcomes.

Since there is only one correct way to arrange the letters to spell 'Geraniums', the number of favorable outcomes is 1.

  1. Calculate the probability.

The probability of a favorable outcome is the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability is:

[tex]\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{9!} = \frac{1}{362880}[/tex]

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