# . In Lotto 6/49, you must pick 6 numbers and pay \$2.00 for each ticket. Six (6) numbers are drawn randomly. The following table summarizes the winning prizes if you match:

6 numbers (1st prize)

## To determine the probability of winning the 1st prize in Lotto 6/49, we need to understand how many possible combinations there are to choose 6 numbers out of 49.

The number of possible combinations, or the total number of ways to choose 6 numbers out of 49, is calculated using the binomial coefficient formula. This formula is denoted by "n Choose k" and is calculated as:

n! / (k! * (n-k)!)

In this case, n = 49 (the total number of available numbers to choose from) and k = 6 (the number of numbers you need to pick).

So, we have:

49! / (6! * (49-6)!)

Expanding the factorials, we get:

49! / (6! * 43!)

Since factorials can be very large numbers, calculating them directly may not be feasible. However, this calculation can be simplified:

49! / (6! * 43!) = (49 * 48 * 47 * 46 * 45 * 44) / (6 * 5 * 4 * 3 * 2 * 1 * 43 * 42 * 41 * 40 * 39 * 38)

Canceling out some terms, we simplify it further:

= (49 * 48 * 47 * 46 * 45 * 44) / (6 * 5 * 4 * 3 * 2 * 1)

This gives us the total number of possible combinations, which is:

13,983,816

Now, since only one combination can be the winning one, the probability of winning the 1st prize is:

1 / 13,983,816

So, the probability of winning the 1st prize in Lotto 6/49 is approximately 0.0000000715 or 1 in 13,983,816.

Keep in mind that this probability does not guarantee winning, as it is still quite low.