Question

In how many ways can the letters
in the word glacier be arranged?

Answer 1

The letters in the word 'glacier' can be arranged in 5040 different ways. This is calculated using the concept of permutations, and since there are no repeating letters, we use 7 factorial (7!) to find the total arrangements.

Step-by-step explanation:

The question "In how many ways can the letters in the word glacier be arranged?" pertains to the mathematical concept of permutations, which is a part of combinatorics. To answer this question, we need to calculate the number of distinct arrangements of the seven letters in the word 'glacier.'

Since there are no repeating letters in the word 'glacier,' each of the letters can occupy any position in the arrangement. The first position can be filled in 7 different ways, the second in 6 ways (once the first letter is placed), and so on, until the last position which can only be filled in 1 way (with the remaining letter). Thus, the total number of ways to arrange the letters is found by multiplying these numbers together: 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 7 factorial (7!).

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.

Therefore, there are 5040 different possible arrangements of the letters in the word 'glacier.'

Answer 2

5,040 times

Step-by-step explanation:

Since there are 7 letters in the word glacier, and there is no set limit, the formula would look like this;

7x6x5x4x3x2x1

(and techinacally 0 counts as 1, but since any number x 1 is itself, it's unnecessary to put it in there)

All of this adds up to 5,040

(I also have acellus and I've already checked it and it's correct )