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. Determine the probability that a randomly selected set of six numbers will win the lottery.

4.167 * 10-6

8.63 * 10-7

5.467 * 10-6

7.15 * 10-8

Will mark branliest

As in this problem the order of numbers does not matter We are talking about a combination and not to permutation.

So to determine the probability that a set of six randomly selected numbers wins the lottery we need to first draw the combination of 6 in 49 without repetition:

C (49.6) = 49! / (6! (49-6) !) = 13983816

Then there are 13983816 combinations of possible numbers for this case.

Finally the probability is:

p = 1/13983816

p = 7,151 x10 ^ - 8

The correct option is the last