how many different ways can the letters of \generally\ be arranged? if the letters of \generally\ are…

how many different ways can the letters of \generally\ be arranged? if the letters of \generally\ are arranged in a random order, what is the probability that the result will be \generally\? the number of different ways that the letters of \generally\ can be arranged is (type an integer or a simplified fraction.) the probability that the random arrangement of letters will result in \generally\ is (type an integer or a simplified fraction.)

how many different ways can the letters of \generally\ be arranged? if the letters of \generally\ are arranged in a random order, what is the probability that the result will be \generally\? the number of different ways that the letters of \generally\ can be arranged is (type an integer or a simplified fraction.) the probability that the random arrangement of letters will result in \generally\ is (type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Calculate total arrangements

The word "generally" has 8 letters. But the letter 'e' appears 3 times. The formula for permutations of a word with repeated letters is $\frac{n!}{n_1!}$, where $n$ is the total number of letters and $n_1$ is the number of times a repeated - letter appears. Here, $n = 8$ and $n_1=3$. So the number of arrangements is $\frac{8!}{3!}=\frac{8\times7\times6\times5\times4\times3!}{3!}=6720$.

Step2: Calculate probability

There is only 1 correct arrangement (the word "generally" itself). The probability $P$ of getting the correct arrangement out of all possible arrangements is the number of favorable outcomes (1) divided by the number of total outcomes. So $P=\frac{1}{6720}$.

Answer:

The number of different ways that the letters of "generally" can be arranged is 6720. The probability that the random arrangement of letters will result in "generally" is $\frac{1}{6720}$.