The first letter can be any one of the 6 letters. For each of those . . .
The second letter can be any one of the remaining 5 letters. For each of those . . .
The third letter can be any one of the remaining 4 letters. For each of those . . .
The fourth letter can be any one of the remaining 3 letters. For each of those . . .
The fifth letter can be any one of the remaining 2 letters.
The total number of different ways they can be arranged is (6 x 5 x 4 x 3 x 2) = 720 .
The number of different ways you can arrange the letters MNOPQ is the number of permutations of 5 things taken 5 at a time. This is 5 factorial, or 120.
The word "house" has 5 distinct letters. The number of ways to arrange these letters is calculated using the factorial of the number of letters, which is 5! (5 factorial). This equals 5 × 4 × 3 × 2 × 1 = 120. Therefore, there are 120 different ways to arrange the letters in the word "house."
The word "fight" consists of 5 distinct letters. The number of ways to arrange these letters is calculated using the factorial of the number of letters, which is 5!. Thus, the total number of arrangements is 5! = 120.
The word "MATH" consists of 4 unique letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 4!. Therefore, the total number of arrangements is 4! = 4 × 3 × 2 × 1 = 24. Thus, there are 24 different ways to arrange the letters in the word "MATH."
The word "prime" consists of 5 distinct letters. The number of permutations of the letters can be calculated using the factorial of the number of letters, which is 5!. Therefore, the total number of ways to arrange the letters in "prime" is 5! = 120.
The number of different ways you can arrange the letters MNOPQ is the number of permutations of 5 things taken 5 at a time. This is 5 factorial, or 120.
The word "monkey" consists of 6 distinct letters. The number of ways to arrange these letters is given by the factorial of the number of letters, which is 6!. Calculating this, we find that 6! = 720. Therefore, there are 720 different ways to arrange the letters in "monkey."
The word "house" has 5 distinct letters. The number of ways to arrange these letters is calculated using the factorial of the number of letters, which is 5! (5 factorial). This equals 5 × 4 × 3 × 2 × 1 = 120. Therefore, there are 120 different ways to arrange the letters in the word "house."
There are 10 letters is the word JOURNALISM. Since they are all different, the number of ways you can arrange them is simply the number of permutations of 10 things taken 10 at a time, or 10 factorial, or 3,628,800.
The word "fight" consists of 5 distinct letters. The number of ways to arrange these letters is calculated using the factorial of the number of letters, which is 5!. Thus, the total number of arrangements is 5! = 120.
The word "prime" consists of 5 distinct letters. The number of permutations of the letters can be calculated using the factorial of the number of letters, which is 5!. Therefore, the total number of ways to arrange the letters in "prime" is 5! = 120.
The word "MATH" consists of 4 unique letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 4!. Therefore, the total number of arrangements is 4! = 4 × 3 × 2 × 1 = 24. Thus, there are 24 different ways to arrange the letters in the word "MATH."
Three
The number of different ways to arrange 4-letter words depends on whether the letters are unique or not. If all 4 letters are unique, the arrangements can be calculated using factorial notation: 4! (4 factorial), which equals 24. If some letters are repeated, the formula adjusts accordingly, dividing by the factorial of the counts of the repeated letters.
No.
Oh, what a lovely word to arrange! Let's see here, with the word "literature," we have 10 letters in total. Since some letters are repeated, we need to account for that in our count. So, there are 10!/(2!2!) = 453600 distinct ways to arrange the letters of "literature" in total. Isn't that just delightful?
The word "TUBONT" consists of 6 distinct letters. The number of ways to arrange these letters is given by the factorial of the number of letters, which is 6!. Therefore, the total number of arrangements is 6! = 720.