mathmath333
  • mathmath333
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?
Mathematics
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mathmath333
  • mathmath333
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?
Mathematics
schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ A dice is rolled six times. }\hspace{.33em}\\~\\ & \normalsize \text{ One, two, three, four, five and six appears on consecutive throws of dices.}\hspace{.33em}\\~\\ & \normalsize \text{ How many ways are possible having 1 before 6?}\hspace{.33em}\\~\\ \end{align}}\)
welshfella
  • welshfella
if 1 occurs on the first throw ether are 5! ways . Agreed? I'm never 100% confident on these counting questions!!
mathmath333
  • mathmath333
ok

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welshfella
  • 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
  • welshfella
* when 1 occurs
welshfella
  • welshfella
so that is -4!
mathmath333
  • mathmath333
negative 4! ?
welshfella
  • welshfella
No sorry - we just ignore those
welshfella
  • welshfella
if no 6 on first throw there are 4 * 4! ways right?
mathmath333
  • mathmath333
how does that come
imqwerty
  • imqwerty
is the answer (5!)^2 ?
welshfella
  • welshfella
well you have any number between 2 and 5 on first throw and there are 4! arrangements of the other 4
mathmath333
  • mathmath333
|dw:1442759227308:dw|
mathmath333
  • mathmath333
in book it is given as 6!/2=360
imqwerty
  • 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
  • mathmath333
A hint is given: out of total 6! half would have 1 before 6
welshfella
  • 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
  • mathmath333
|dw:1442759844597:dw|
imqwerty
  • imqwerty
a typo :) there must be some erase tool :)
imqwerty
  • imqwerty
nd yes cx outta those 6! ways half wuld hav 1 before 6 i never thought that
mathmath333
  • mathmath333
i m unable to digest the hint
imqwerty
  • imqwerty
ok tell- in how many ways can u arrange 6balls in a line?
mathmath333
  • mathmath333
6!
imqwerty
  • imqwerty
and how many of these ways will have ball number 1 before ball 6
mathmath333
  • mathmath333
half
imqwerty
  • imqwerty
can u relate this situation with the situation we have int he problem :)
mathmath333
  • mathmath333
u replaced ball with dice
imqwerty
  • imqwerty
yes :) did u get the hint now
mathmath333
  • mathmath333
|dw:1442760669616:dw|
mathmath333
  • mathmath333
ur pic matches with the above lol
imqwerty
  • imqwerty
:)
imqwerty
  • imqwerty
m soon gonna change it wid an owl pic :)
imqwerty
  • imqwerty
wait hey that is blank nd my pic is not blank :)
Nnesha
  • Nnesha
right click on the screenshot *open image in new tab* then copy paste that url into draw (mathmath333)

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