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:
- 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]
- 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.
- 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]
