To find the number of 5-letter permutations that can be made from the letters of the word 'ORGANIC,' you 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, you have 7 letters in the word 'ORGANIC,' and you want to find 5-letter permutations, so n = 7 and r = 5.
P(7, 5) = 7! / (7 - 5)!
Now, calculate the factorials:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
(7 - 5)! = 2! = 2 x 1 = 2
Now, plug these values into the formula:
P(7, 5) = 5040 / 2 = 2520
So, there are 2520 different 5-letter permutations that can be made from the letters of the word 'ORGANIC.' Therefore, the correct answer is (a) 2520.