Which expression would you use to figure out the number of ways you can arrange the letters in the word equation?

A. 8!
B. 8P4
C. 4P8
D. 4!

1 answer

B. 8P4

Explanation:

When dealing with permutations, where the order matters and repetition is not allowed, we use the formula:

nPr= n!/(n-r)!

In this case, we have 8 letters in the word "equation" and want to know how many ways we can arrange 4 letters at a time. So:

n = 8 (the total number of letters)

r = 4 (the number of letters being arranged)

Therefore, the expression to use is 8P4, which can be calculated as:
8P4 = 8!/(8-4)! = 8!/4! = (8×7×6×5)/(4×3×2×1) = 1680

So, there are 1680 ways to arrange the letters in the word "equation" if we choose 4 letters at a time.