Question

Help please!? How many permutations are there for the letters in the word SUCCESSES?
a. 362,880

b. 22,680

c. 7560

d. 3780
my answer: a. 362,880
I got that b/c i did this 9! b/c there were 9 letters so i got 9*8*7*6*5*4*3*2*1=362,880... am i right? cuz i got kinda confused... :/

Answer 1

Please explain too! :) Thank you!!! :)

Answer 2

hi @jim_thompson5910 thanks for coming to help too :)

Answer 3

successes has 9 letters yes BUT

s repeats 4 times
e repeats twice
c repeats twice

therefore it should be \[\large \frac{9!}{4!2!2!}\]

Answer 4

i am confused... :( so what is the answer and why? Shouldn't it be A? what do you think @jim_thompson5910

Answer 5

so you get \[\large \frac{9 \times 8 \times 7 \times 6 \times 5 \times \cancel{4!}}{\cancel{4!}2!2!} = \frac{9 \times 8 \times 7 \times 6 \times 5}{2 \times 2}\]

Answer 6

It's not A. Keep in mind that you have 2 Cs. So if you simply do 9! = 362880, you're overcounting because CC is the same as CC

So you need to divide by 2! = 2 to correct for this overcounting


You need to do the same for the Es as well. So divide by 2! = 2


Finally, you have 4 letters that are an S. So you need to divide by 4! = 24

Answer 7

So divide 9! = 362880 by 2*2*24 = 96 to get

362880/96 = 3780

Answer 8

a blue owl comes to help and they ask for the gray one lol

Answer 9

So the answer is d. 3780?? for sure?? 100%????

Answer 10

yeah it's d

Answer 11

yes I'm 100% sure

Answer 12

If you want, you can try this idea with a smaller word that has repeating letters

Answer 13

YAy! thanks so much!! Now i understand it haha it's because the letters are repeating so you have to divide by 4!2!2! ???

Answer 14

exactly

Answer 15

awesome! thanks! :)

Answer 16

sure thing

Answer 17

like for example LGBASALLOTE has 11 letters and L repeats thrice and A repeats twice so you'll get \[\frac{11!}{3!2!}\] i just wanted to say my name :p

Answer 18

lol! thanks! :)