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?

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- mathmath333

- schrodinger

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

- welshfella

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

- mathmath333

ok

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## More answers

- 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

- welshfella

* when 1 occurs

- welshfella

so that is -4!

- mathmath333

negative 4! ?

- welshfella

No sorry - we just ignore those

- welshfella

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

- mathmath333

how does that come

- imqwerty

is the answer (5!)^2 ?

- welshfella

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

- mathmath333

|dw:1442759227308:dw|

- mathmath333

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

- 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

- mathmath333

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

- 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

- mathmath333

|dw:1442759844597:dw|

- imqwerty

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

- imqwerty

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

- mathmath333

i m unable to digest the hint

- imqwerty

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

- mathmath333

6!

- imqwerty

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

- mathmath333

half

- imqwerty

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

- mathmath333

u replaced ball with dice

- imqwerty

yes :) did u get the hint now

- mathmath333

|dw:1442760669616:dw|

- mathmath333

ur pic matches with the above lol

- imqwerty

:)

- imqwerty

m soon gonna change it wid an owl pic :)

- imqwerty

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

- Nnesha

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

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