artofspeed 3 years ago hard probability question.. help plz?

1. artofspeed

2. artofspeed

I dunno :S

3. kevinkeegan

\[4^{4} = 256\]

4. kevinkeegan

want me to explain?

5. shivam_bhalla

6. kevinkeegan

okay you have 4 choices tiles to use WWW WWB WBWetc... each will take up 3 slots and you have 10 slots only so we use 3 diff groups( groups as in WWW= 1grp, WBW=1grp an so on) first, taking up 9 slots, so the probability of arranging the 3 grps = 4X4X4 ; now we left with 1 last slot for the single white tile; and we can put the white tiles @ 4 different places( trying drawing out): so that gives us extra 4 different combos and therefore, total probability= 4X4X4X4

7. kevinkeegan

|dw:1335113090901:dw| arrow point to last slot for single white tile

8. ParthKohli

I know the answer. http://ptri1.tripod.com/ptreal1r.gif See this picture of a pascal's triangle. Now see the row 2 and sum all the numbers of row 2 You get 4! See the row 10 and get the sum of all the numbers in row 10. You get the answer!

9. kevinkeegan

one thing to note: question did not state if the tiles can be reused, if cannot reuse, answer is 4X3X2X4

10. ParthKohli

11. artofspeed

12. kevinkeegan

pascal triangle does not work here becasue the tiles are in groups of 3

13. ParthKohli

14. kevinkeegan

15. ParthKohli

The final line, see it.

16. kevinkeegan

is they want us to use the 4 combo of WWW WWB WBW BWW then im right

17. kevinkeegan

if*

18. shivam_bhalla

Somebody please explain the question. It is confusing

19. kevinkeegan

they want u to use the combos to fill up the 10 slots

20. ParthKohli

They're asking us the different colour patterns in a ten by one rectangle. There are 1024 such patterns. Try it on your own.

21. ParthKohli

They're asking us about the number of patterns possible in this case.

22. kevinkeegan

last line : "using THESE TILES " and i suppose THESE TILES refer to the 4 different colour patterns

23. kevinkeegan

the tiles are not individual they come in sets

24. ParthKohli

All right. You're right, I'm wrong. Okay?

25. kevinkeegan

|dw:1335113911913:dw|

26. artofspeed

@kevinkeegan, 'these tiles' actually refer to the 3 tiles in the picture

27. kevinkeegan

yep and the 3 tiles form the 4 colour patterns they giv WWW WBW BWW WWB

28. PaxPolaris
29. niki

hey i think the ans is 385 plz check