Question

One of the UK lottery systems consists of selecting six numbers from forty-nine for a one-pound stake. The winning numbers are drawn at random and the order is not important. The probability that a randomly selected set of six numbers will win the lottery is 0.0000000715. True or False

Answer 1

The number of ways you can choose "r" things from a larger set of "n" things:
n! / r! * (n -r)! =
49! / 6! * (43!) =
49 * 48 * 47 * 46 * 45 * 44 * 43! / 6! * 43! =
49 * 48 * 47 * 46 * 45 * 44 / 6 * 5 * 4 * 3 * 2 =
49 * 47 * 46 * 45 * 44 / 5 * 3  =
49 * 47 * 46 * 3 * 44 =
13,983,816
So it is 1 in 13,983,816 and
p =  0.00000007151123842019

So, it is true.