264 million in possible winnings please find the probability

264 million in possible winnings, please find the probability. Players may pick 6 numbers from 2 seperate pools of numbers - 5 from 1 through 56 and 1 from 1 through 46. You win the jackpot by matching all six winning numbers. Find the probability of winning.

Solution

264 million in possible winnings, please find the probability.

P=1/264 million

Players may pick 6 numbers from 2 seperate pools of numbers - 5 from 1 through 56 and 1 from 1 through 46. You win the jackpot by matching all six winning numbers. Find the probability of winning.

selecting 5 numbers from 56,

n = 56   r = 5 (56C5)

selecting 1 number from 46,

n = 46   r = 1    (46C1)

(56C5)* (46C1)= 3819816*46=175711536

The probability of winning the jackpot is
      1/175711536

=0.000000005