## Ishaan94 3 years ago A simple combinatorics problem. Word 'SUCCESS'. Number of ways such that no two Ss and Cs are together.

1. Ishaan94

@eliassaab @blockcolder

2. THE_PROPHET

my guess is 360....idk if i solved it rite....anyone??

3. Ishaan94

360!?! :o How?

4. THE_PROPHET

well its wrong sry!!

5. Ishaan94

Of course it is.

6. ganeshie8

396 ?

7. Ishaan94

Noway Dude

8. THE_PROPHET

factorial of 6??

9. Ishaan94

Nope

10. Ishaan94

Stop guessing. Take your time and work on the problem.

11. Ishaan94

And for your information, this problem is not some challenge. I don't know how to do it. So you will have to show your work.

12. THE_PROPHET

|dw:1340534838304:dw| can be interchange so that no S are together in only 2 ways........ |dw:1340534915656:dw| 6 spaces can be filled by 2 Es in ....6c3/2 ways...... |dw:1340534979616:dw|.. so final answer is 15

13. Ishaan94

No the answer is not 15.

14. blockcolder

The complement of "no 2 S's and C's are together" is "2 S's or C's are together." 2 S's or C's together = 2 S's together + 2 C's together - 2 S's and 2 C's together 2 S's together = 5! by considering the 3 s's as 1 2 C's together = 6! by considering 2 c's as 1 2 S's and 2 C's together = 4! So it's 7!-(5!+6!-4!)=4224 ways.

15. KRAZZy

Number of Letters/Characters in the word "SUCCESS" = 7 {S, U, C, C, E, S, S} No. of Letters : of the first kind ⇒ No. of S's = 3 ⇒ a = 3 of the second kind ⇒ No. of C's = 2 ⇒ b = 2 which are all different = 2 {U, E} ⇒ x = 2 = n=7!/3! × 2! = 7 × 6 × 5 × 4 × 3 × 2!/3 × 2 × 1 × 2! = 7 × 6 × 5 × 4 × 3 = 2,520

16. Ishaan94

blockcoder you are including too many repetitive arrangements

17. ganeshie8

answer cannot be more than 420

18. Ishaan94

_S_S_S_ 4 spaces, 4 choices {C, C, E, U}. 4!/2! = 4*3 = 12. S_S_S__ -> 12 __S_S_S -> 12 So, 12 + 12 + 12 = 36. Haha Got it. Thanks all.

19. THE_PROPHET

yeah i got it thanks!!

20. Callisto

21. Ishaan94

:(

22. Ishaan94

I think, I included two repetitions

23. Ishaan94

Ohh CCS_S_S and S_S_SCC isn't possible. It still comes out to be 36. Thanks Callisto.

24. Callisto

If.... you have time.... and if ..... you don't mind, can you explain??