Question

Find the number of permutations of the letters of the word LOOPHOLE

Answer 1

3360 I believe. If I remember correctly, you should use the nPr formula to solve this :]

Answer 2

Answer:

6!/3!=6x5x4x3x2/3x2=6x5x4=120

Step-by-step explanation:

There are L, O, O, P, H, O, L, E; 8 letters in LOOPHOLE. However, three letters repeat: OOO. That means we cannot count them as different and use ! for them.

L,P,H,L,E,O are the letters not double counted. There are SIX letters, so 6!, however, you still have to divide since there are the Os you have to consider.

You have to divide by 3! as they repeat 3 times.

Thus, 6!/3!

"There is a subset of permutations that takes into account that there are double objects or repetitions in a permutation problem. In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical" -www. ck12. org > probability > lesson > permutation