Probability (I have no idea..)?

Question

In how many ways can the letters of the word FACETIOUS be arranged in a line.

This part I know how to do. Answer is 9979200.

*** What is the probability that the two I's are separated.

[This is the part that I don't understand and have no idea on. =.= Please help by showing your workings clearly and explain (:]

By the way, the answer is 9/11.

Thanks.

Answer 1

there's only one I?!

in probability:

we want the two i's to be apart. instead. let's find out how many combinations there are where the two i's are together, and subtract this form the total possible combinations.

if the two i's are together, we count them as one letter, which can be arranged in 2! ways. therefore, there are 10 letters. so the total number of ways is 10!*2!

so, the total number of possibilities where the i's are not toegether=

total number - 10!2! = 11!-10!2! = 39916800 - 7257600

=32659200

therefore, probablility= 32659200/11!

=81.81818181%

Answer 2

there is only 1 'i' in the word~!

AM

Answer 3

I was wondering how *** FACETIOUS wud give u 9979200 adn where is d second i

okay d word is probability.... d answer wud be lyk dis

1-(2*10!/11!) = 9/11

find d prob dat i is together and den 1- it wud give ya d answer...... for dat at first take d 2 i's as 1.