Respuesta :
Answer:
336 arrangements
Step-by-step explanation:
the word ABSOLUTE has 8 individual letters
we are asked to pick 3 letters out of 8 letters and we note that in this case, the order of the letters matter, hence we have to permutate 3 letters of 8
₈P₃ = 8! / (8-3)!
= 8! / 5!
= 336 arrangements
Edit: fixed spelling
We will find that there are 336 different 3-letter arrangements.
In the word ABSOLUTE we have a total of 8 different letters, from these, we want to select 3, and then we want to order the 3 letters.
So the number of different groups of 3 letters that we can take out of the set of 8 letters is:
[tex]C(8, 3) = \frac{8!}{(8 - 3)!*3!} = \frac{8*7*6}{3*2} = 56[/tex]
Then we want to find the number of ways in which we can arrange these 3 letters.
Let's say that we have 3 places and 3 letters:
- For the first one, we have 3 options.
- For the second one, we have 2 options (one is already in the first place)
- For the third one, we have 1 option.
The number of permutations is given by the product between the numbers of options, we will get:
P = 3*2*1 = 6
The total number of different arrangements is equal to the product between the number of different sets of 3 letters that we can make, and the permutations of these 3 letters, so we have:
C = 6*56 = 336
If you want to learn more, you can read:
https://brainly.com/question/25606878