## Ishaan94 3 years ago Number of ways the word 'SUCCESS' can be arranged, such that no two S's and C's are together. @Zarkon

1. Ishaan94

And @siddhantsharan

2. Chumku

\[7!/2!3!\]

3. siddhantsharan

Hold on. No. 120 - 24 = 96?

4. Ishaan94

I can't be sure of the answer. To convince me you would need to show working as well.

5. Ishaan94

In my textbook 36 is the given answer. But I don't think it's right, now that siddhant and another guy I knew answered 96 instead.

6. Chumku

no. of letters= 7 no. of s = 3 no. of c = 2 therfore no. of combination= 7!/2!3!

7. Ishaan94

8. Ishaan94

know*

9. Chumku

oh i get it sorry

10. Ishaan94

lol :( Byron left me an complicated answer. Integral and stuff.

11. Ishaan94

a*

12. Ishaan94

siddhan can you post the solution as well? or, a hint.

13. Ishaan94

siddhant*

14. siddhantsharan

Yeahhh. Sorry. Do you want the solution or hint?

15. siddhantsharan

Actually since you're not sure, I think I should post my solution. I may be wrong. So, No. of cases with no two C's together and no two S's together = No. of cases with no two S's together ( C's can me arranged anyhow) - No. of cases with no two S's together ( C's being together now)

16. siddhantsharan

Does that seem correct so far? @Ishaan94

17. Ishaan94

It does

18. siddhantsharan

|dw:1340389706521:dw| Writing the letters with spaces between them. And only putting S's in the spaces so as to ensure their seperation. Total ways of doing this ( S's together C's anyhow) : 5C2 * 4!/2!

19. Ishaan94

And it also proves how simple this problem could be

20. Ishaan94

And how stupid I think at times -sigh-

21. siddhantsharan

Yeah. It's pretty simple now.

22. Ishaan94

Thank you

23. siddhantsharan

Anytime :)