Combinations Q

1- In how many ways can you arrange the letters of the word CONGRESS?

2- In how many of these arrangements are the two Ss not together?


I have the answers, but I need an explanation. Thanks.

1.) For a word with 7 different letters you have 7! posibilities to arrange the letters (5040). Because you have two identical letters, there are only half of that different outcomes. 2520.
2.) To have the two"SS" together just look at them as one letter, so you have 6! possobilities 720.

The word has 8 letters, thus 8!.

Which has 40320 possible combinations.

The second time doing such a stupid mistake, someone should this year ended (espacially the "working" part of it!)

1- In how many ways can you arrange the letters of the word CONGRESS?

8 letters, 2 REPEATING

so its 8!/2!


2- In how many of these arrangements are the two Ss not together?

let the two S be together. treat them as a single block. so you have 7 blocks ("C","O","N",...,"E","SS")
you have then: 7!
so if they can't be together, just subtract it off the total:
ie: 8!/2!-7!

you work out the numerical answers.

Thanks. Understood.