12. How many different arrangements can be made with the letters from the word MATH? (1 point)
There are 24 different arrangements that can be made with the letters from the word MATH.
To find the number of different arrangements that can be made with the letters from the word MATH, we can use the concept of permutations.
The word MATH has 4 letters.
To find the number of arrangements, we need to calculate 4 factorial (4!).
4! = 4 x 3 x 2 x 1 = 24
Therefore, there are 24 different arrangements that can be made with the letters from the word MATH.
To find the number of different arrangements that can be made with the letters from the word "MATH," you can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. To calculate the number of permutations, you need to consider the total number of letters and the number of repetitions of each letter.
In the word "MATH," there are 4 letters in total. However, there are repeated letters in this word: "M" appears twice.
To calculate the number of permutations, you can use the formula:
P = n! / (n1! * n2! * ... * nk!)
Where P is the number of permutations, n is the total number of letters, and n1, n2, ... nk represent the number of repetitions for each letter.
In this case, n is 4 (the total number of letters), and n1 (the number of repetitions of the letter "M") is 2. So the formula becomes:
P = 4! / (2!)
Calculating this, you have:
P = 4 * 3 * 2 * 1 / (2 * 1)
Simplifying further:
P = 24 / 2
P = 12
Therefore, there are 12 different arrangements that can be made with the letters from the word "MATH."