## vishweshshrimali5 5 years ago A fair die is rolled four times. The probability that each of the final three rolls is at least as large as the roll preceeding it is m/n in the lowest terms. Then n -10m = ?

1. anonymous

Please stop spamming and wait patiently for a tutor to assist you with your problems.

2. vishweshshrimali5

KKKKKKK sorry

3. vishweshshrimali5

Hey!! Xcuseme Who are you polpak ? May I know please?

4. anonymous

Just a lego guy

5. vishweshshrimali5

What is lego guy ?

6. vishweshshrimali5

I mean what does it mean ?

7. vishweshshrimali5

Hey You have 580 medals !!!!!!!!!! wow

8. anonymous

this question is a poser

9. anonymous

Others have more.

10. vishweshshrimali5

11. vishweshshrimali5

What is a poser !

12. anonymous

are u studying iit coaching

13. vishweshshrimali5

No but preparing for that but how do u know that man ?

14. anonymous

if the first roll is a1, then probability is 1 if the first roll is a 2 then probability is $(\frac{5}{6})^3$

15. anonymous

that type of question comes in iit

16. vishweshshrimali5

Yaa u are right amingad !

17. anonymous

it is easy take 4 turn as 36c4

18. vishweshshrimali5

How do u got that satellite please explain !

19. anonymous

oh wait that is wrong. i need to read more carefully

20. vishweshshrimali5

21. vishweshshrimali5

How do you got that amingad

22. anonymous

looks like coupon collectors problem

23. vishweshshrimali5

It may be

24. anonymous

what is probability of a record. gives harmonic series

25. anonymous

yikes now i have to think

26. vishweshshrimali5

Amingad please explain step by step I can't understand it so fastly

27. vishweshshrimali5

I am a neophyte in this field you may think that

28. anonymous

fair dice consist of 6 numbers . so the the no of times get the highest probability of number will be 24 c4 my mistake i wrote 36 c4

29. anonymous

you lost me here for sure

30. vishweshshrimali5

What do you mean to say satellite ?

31. vishweshshrimali5

Okkkkk amingad now is there any step left ?

32. anonymous

i mean i am lost completely.

33. vishweshshrimali5

Ohhhh you mean that it is a nice question then thanks a lot

34. vishweshshrimali5

Well satellite you can have a look at other questions

35. anonymous

12c3< m/ n so n has to be highest dice to be rolled

36. vishweshshrimali5

37. anonymous

yep it is tricky but good

38. vishweshshrimali5

can you write the answer in a single post and with each step explained Because my teacher says that you will have to answer the question with each step explained or you will get no marks

39. vishweshshrimali5

Will you please do so ?

40. vishweshshrimali5

41. Zarkon

$\frac{7}{72}$

42. anonymous

43. Zarkon

i know

44. Zarkon

Just for fun...if we used an n-sided die the probability is $\frac{(n+1)(n+2)(n+3)}{24n^3}$

45. Zarkon

and if we rolled an n-sided die k times it would be $\frac{n(n+1)(n+2)\cdots(n+k-1)}{n^{k}k!}$