How many different arrangements can be made with the letters from the word ORANGE?
A 24 *
B 32
C 60
D 120
None of the offered is true.
When the letters are different the number of arrangements is 6!
6! = 1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ 6 = 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. A permutation is an arrangement of objects where the order matters.
The word ORANGE has 6 letters. To find the number of different arrangements, we need to calculate the number of permutations of 6 letters taken all at a time.
Step 1: Calculate the total number of permutations.
The formula to calculate the number of permutations of n objects taken all at a time is given by n!.
In this case, n = 6.
So, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Step 2: Account for repeated letters.
In the word ORANGE, the letter 'E' is repeated twice. When we calculate permutations, the repeated letters need to be divided by the factorial of how many times each letter repeats.
In this case, 'E' repeats twice.
So, we need to divide the total number of permutations (720) by 2!.
2! = 2 x 1 = 2
720 / 2 = 360
Therefore, there are 360 different arrangements that can be made with the letters from the word ORANGE.
So, the correct answer is D) 360.