How many different words can be formed with the letters SCHOOL? (The words formed do not have to be real words.)
6!/2! = 360
To find the number of different words that can be formed with the letters in "SCHOOL," we need to determine the total number of permutations.
The word "SCHOOL" has 6 letters, so we have 6 positions to fill.
The first position can be filled with any of the 6 letters. After selecting one letter, we have 5 remaining letters to choose from for the second position. Similarly, for the third position, we have 4 letters to choose from, and so on.
Using the multiplication principle, we multiply the number of options for each position:
6 × 5 × 4 × 3 × 2 × 1 = 720
Therefore, there are 720 different words that can be formed with the letters in "SCHOOL."
To find the number of different words that can be formed with the letters in the word "SCHOOL," we need to determine the number of permutations.
The word "SCHOOL" has a total of 6 letters. To calculate the number of permutations, we can use the formula for permutations of a set:
P(n, r) = n! / (n - r)!
where n is the total number of items and r is the number of items taken at a time.
In this case, we have 6 letters and we want to arrange all of them, so n = 6 and r = 6. Plugging these values into the formula, we get:
P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
Since 0! is equal to 1, we have:
P(6, 6) = 6! / 1
= 6!
To calculate 6!, we multiply 6 by all the positive integers less than 6:
6! = 6 × 5 × 4 × 3 × 2 × 1
= 720
Therefore, there are 720 different words that can be formed with the letters in the word "SCHOOL."