How many different arrangements can be made with the letters from the word ORANGE?

all the letters are different, so the number of arrangements is simply 6! or 720

To find the number of different arrangements that can be made with the letters from the word "ORANGE," we can use the concept of permutations.

Step 1: Determine the number of letters in the word.
The word "ORANGE" has 6 letters.

Step 2: Calculate the factorial of the number of letters.
The factorial is denoted by "!" and represents the product of all positive integers less than or equal to the given number. In this case, we need to calculate 6!.

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 different arrangements that can be made with the letters from the word "ORANGE."

To find the number of different arrangements that can be made with the letters from the word "ORANGE," you can use the concept of permutations.

First, count the number of letters in the word "ORANGE." There are 6 letters.

Since the letters in "ORANGE" are not all unique (i.e., there are repeated letters), we need to consider the repeated letters when calculating the arrangements.

In this case, there are 2 repetitions: the letter "R" and the letter "E."

To find the number of arrangements, you can use the formula for permutations with repeated elements:

n! / (n1! * n2! * ... * nk!)

Where n is the total number of letters, and n1, n2, ..., nk are the numbers of repetitions for each repeated letter.

In the case of "ORANGE," n is 6, n1 (for "R") is 2, and n2 (for "E") is also 2.

So, the calculation would be:

6! / (2! * 2!) = 720 / (2 * 2) = 720 / 4 = 180

Therefore, there are 180 different arrangements that can be made with the letters from the word "ORANGE."