How many permutations are there of the word "MATH"?

How many permutations are there of the word "MATH"?

• A. 12
• B. 20
• C. 24
• D. 30

Answer: (C)

To find the number of permutations of the letters in the word "MATH", we note that the word consists of 4 distinct letters: M, A, T, and H. The total number of ways to arrange these letters is calculated using the factorial of the number of letters. The formula for the permutations of \(n\) distinct objects is \(n!\), where "!" (factorial) represents the product of all positive integers up to \(n\). In this case, we have 4 letters, so we use \(4!\): \[ 4! = 4 \times 3 \times 2 \times 1 = 24. \] This means there are 24 unique arrangements of the letters in "MATH". Each arrangement uses all letters, and since there are no repeating letters, each arrangement is distinct. Thus, the number of permutations of the word "MATH" is indeed 24.

To find the number of permutations of the letters in the word "MATH", we note that the word consists of 4 distinct letters: M, A, T, and H. The total number of ways to arrange these letters is calculated using the factorial of the number of letters.

The formula for the permutations of (n) distinct objects is (n!), where "!" (factorial) represents the product of all positive integers up to (n). In this case, we have 4 letters, so we use (4!):

[

4! = 4 \times 3 \times 2 \times 1 = 24.

]

This means there are 24 unique arrangements of the letters in "MATH". Each arrangement uses all letters, and since there are no repeating letters, each arrangement is distinct.

Thus, the number of permutations of the word "MATH" is indeed 24.