How many arrangements can be made using 2 letters of the word HYPERBOLAS if no letter is to be used morethan once?
A) 90
B) 1,814,400
C) 45
D) 3,628,800

Question

Quizplus · Accepted Answer

The word HYPERBOLAS has 10 distinct letters. The number of ways to arrange 2 letters from these 10 is calculated using permutations since the order matters. The formula for permutations of n items taken r at a time is nPr = n! / (n-r)!. For this case, it's 10P2 = 10! / (10-2)! = 10! / 8! = 10 * 9 = 90.

How Many Arrangements Can Be Made Using 2 Letters of the Word