## mathmath333 one year ago A dice is rolled six times. One, two, three, four, five and six appears on consecutive throws of dices. How many ways are possible having 1 before 6?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ A dice is rolled six times. }\hspace{.33em}\\~\\ & \normalsize \text{ One, two, three, four, five and six appears on consecutive throws of dices.}\hspace{.33em}\\~\\ & \normalsize \text{ How many ways are possible having 1 before 6?}\hspace{.33em}\\~\\ \end{align}}

2. welshfella

if 1 occurs on the first throw ether are 5! ways . Agreed? I'm never 100% confident on these counting questions!!

3. mathmath333

ok

4. welshfella

so I guess we have to consider the scenario when occurs on the second throw. when 6 occurs on the first throw we have to discount these arrangements

5. welshfella

* when 1 occurs

6. welshfella

so that is -4!

7. mathmath333

negative 4! ?

8. welshfella

No sorry - we just ignore those

9. welshfella

if no 6 on first throw there are 4 * 4! ways right?

10. mathmath333

how does that come

11. imqwerty

12. welshfella

well you have any number between 2 and 5 on first throw and there are 4! arrangements of the other 4

13. mathmath333

|dw:1442759227308:dw|

14. mathmath333

in book it is given as 6!/2=360

15. imqwerty

sry i did a silly mistake well- |dw:1442759335031:dw| like this make cases nd then u get tota ways= 5!+4*4!+3*4!+2*4!+1*4!=360

16. mathmath333

A hint is given: out of total 6! half would have 1 before 6

17. welshfella

if 1 is middle number there are 72 ways also if 72 for 2 is 4th so we have 120 + 96 + 72 + 72 = 360

18. mathmath333

|dw:1442759844597:dw|

19. imqwerty

a typo :) there must be some erase tool :)

20. imqwerty

nd yes cx outta those 6! ways half wuld hav 1 before 6 i never thought that

21. mathmath333

i m unable to digest the hint

22. imqwerty

ok tell- in how many ways can u arrange 6balls in a line?

23. mathmath333

6!

24. imqwerty

and how many of these ways will have ball number 1 before ball 6

25. mathmath333

half

26. imqwerty

can u relate this situation with the situation we have int he problem :)

27. mathmath333

u replaced ball with dice

28. imqwerty

yes :) did u get the hint now

29. mathmath333

|dw:1442760669616:dw|

30. mathmath333

ur pic matches with the above lol

31. imqwerty

:)

32. imqwerty

m soon gonna change it wid an owl pic :)

33. imqwerty

wait hey that is blank nd my pic is not blank :)

34. Nnesha

right click on the screenshot *open image in new tab* then copy paste that url into draw (mathmath333)