To find the number of distinct letter arrangements that can be made from the word "LETTER" with each "T" on each side, we can break down the problem into separate steps.
Step 1: We have to consider that there are two "T"s in the word "LETTER" that are fixed in their positions. The other four letters are "L", "E", "E", and "R". We need to find the number of arrangements for these four letters alone.
Step 2: For the four remaining letters ("L", "E", "E", and "R"), we can find the number of distinct arrangements by using the formula for the number of arrangements of objects with repetition.
The formula for the number of arrangements of objects with repetition is n!, divided by the product of the factorials of the repeated elements, where n is the total number of objects. In this case, n = 4.
So, using this formula:
Number of arrangements = 4! / (2! * 1! * 1!)
The factorials of the repeated elements "E" and "R" are 1, since they are not repeated more than once.
Simplifying:
Number of arrangements = (4 * 3 * 2 * 1) / (2 * 1 * 1) = 24 / 2 = 12
Therefore, there are 12 distinct letter arrangements that can be made from the word "LETTER" with each "T" on each side.
So the correct answer to the question is (B) 12.
Hope this helps!