Question

Consider a lottery system where players select four distinct numbers from 1 to 17, and then two distinct capital letters from the standard English alphabet. An example ticket is (4 5 16 17 A B). Entries are automatically presented in numerical order and alphabetical order, so the order in which a contestant selects their entries does not matter. Determine, with justification, the probability a ticket matches ATLEAST THREE WINNING SELECTIONS

Answer 1

Step 1:
Total number of tickets:

First entry = 17 ways

Second entry = 16 ways

Third entry = 15 ways

Fourth entry = 14 ways

Fifth entry = 26 ways

Sixth entry = 25 ways.

So,

number of tickets = 17 X 16 X 15 X 14 X 26 X 25 = 37,128,000

Tickets matching ATLEAST THREE WINNING SELECTIONS = THREE WINNING SELECTIONS + FOUR WINNING SELECTIONS + FIVE WINNING SELECTIONS =

So,

P(a ticket matches ATLEAST THREEWINNING SELECTIONS) = 16/37,128,000 = 0.000000004309

                                                                                           = 0.4309 X 10^-8