Using the letters in the word FABRIC, find the number of permutations that can be formed using 2 letters at a time. Show your work or explain how you got your answer.
To find the number of permutations that can be formed using 2 letters at a time from the word "FABRIC", we can use the formula for permutations of n objects taken r at a time, which is given by:
P(n,r) = n! / (n - r)!
In this case, we have a total of 6 letters in the word "FABRIC" (n = 6), and we want to find the number of permutations using 2 letters at a time (r = 2).
P(6,2) = 6! / (6 - 2)!
= 6! / 4!
= (6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)
= (6 x 5)
= 30
Therefore, there are 30 permutations that can be formed using 2 letters at a time from the word "FABRIC".