In a state lottery game you pick six of the numbers 1 throug

In a state lottery game, you pick six of the numbers 1 through 49, and then in a televised
drawing six of these numbers are selected. If all six of your numbers are selected then you win a share
of the first prize. What is the probability that you will win a share of the first prize?

Solution

number of ways of picking 6 numbers from 49 numbers = 49C6
    = 49! /(6! * (49-6)!)
   = 49! /(6! * 43!)
   =13983816

one of this selection wins the 1st prize

Probability= number of favourable case/ total number of cases

=1/ 13983816