How to culculate the probability to strike TOTO?

TOTO is a lottery. The total available numbers are from 1 to 45. Only 6 numbers will be drawn. If all the 6 numbers match, you win the first prize! The 6 numbers will not repeated. How to culculate the probability to strike the 1st prize?|||the calculations, use the method n C r or n CHOOSE r=


45 Choose 6= 8,145,060





these are factorials that break down to


45*44*43*42*41*40/6*5*4*3*2*1 = 8,145,060|||The total number of 6-combinations from a set of 45 numbers is:





C(45, 6) = 45 x 44 x 43 x 42 x 41 x 40 / (6 x 5 x 4 x 3 x 2 x 1)





or 8145060





So your chances are 1 in 8145060.|||Since the order does not matter, this is a combinations problem. There are 6 correct numbers and you need all 6 so the top of the probability fraction is 6C6.





There are 45 total numbers so the bottom is 45C6|||There are C(45,6) ways to select 6 numbers, that is 45*44*43*42*41*40/6!.





There is only one good choice(matching all six numbers).





So probability is 1/C(45,6) = 1/8145060.|||probablility = possible outcome/ all outcome


P(1st prize)=1/(45C6)=1/8145060|||To translate all those other correct answer, odds are a little worse than one in eight million.