Probability Question

[snoopy1239]

It's been a while since I've done my maths GCSE ('O' Level for the oldies), but was wondering if anyone knew how to work out this question:

If, on average, I cash in 1 in 5 and play 12 tournaments, what are the chances that I will make the money in a minimum (not exactly) of 6 events?

I gave it a crack but tied myself up in knots.

[DungBeetle]

n!   Success   r!   (n-r)!   Cominations      Probability 1 combo   Probability all combos
479,001,600    6   720   720   924      1.67772E-05   0.015502148
   7   5040   120   792      4.1943E-06   0.003321889
   8   40320   24   495      1.04858E-06   0.000519045
   9   362880   6   220      2.62144E-07   5.76717E-05
   10   3628800   2   66      6.5536E-08   4.32538E-06
   11   39916800   1   12      1.6384E-08   1.96608E-07
   12   479001600      1      4.096E-09   4.096E-09

                     1.94%

[DungBeetle]

Formula needed is n!/r!(n-r)! to work out your combinations and then easy from there.

[snoopy1239]

Cool. Many thanks. Please excuse my stupidity, but can you confirm the values in the above formula (i.e. what does 'r' reference?)?

[DungBeetle]

n!  = total number of combinations i.e. 12x11x10x9x8x7x6x5x4x3x2x1
r! = number of combinations for 6 wins i.e. 6x5x4x3x2x1
(n-r)! = number of unchosen combinations i.e. (12-6) = 6x5x4x3x2x1

The formula then gives you total combinations for posting 6 wins in 12 tournaments.  You then work out the probability of winning 6 tournies and multiply by total possible combos to get total probabilty you post 6 wins.

You then do 7 wins, 8 wins etc.

Then add them all up.

[snoopy1239]

Ta. Much appreciated.