How many different arrangements of two letters can
you make from the letters in the word problem, if no repetition
of letters is allowed?
You have not provided us with the word problem that contains the letters.
To find the number of arrangements of two letters without repetition from the word "problem," we can use the concept of permutations.
First, let's count the number of distinct letters in the word "problem." We have six distinct letters: P, R, O, B, L, and E.
Next, we need to choose 2 letters from the 6 distinct letters. We can calculate this using the formula for combinations. The formula for combinations is nCr, where n represents the total number of distinct objects and r represents the number of objects chosen. In this case, we have 6 distinct letters, and we want to choose 2 letters. So the formula for the number of combinations is:
C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = 6 * 5 / 2 * 1 = 15.
Therefore, there are 15 different arrangements of two letters that can be made from the letters in the word "problem" without repetition.