What is the probability of winning the jackpot prize in the Philippine Lotto 6/42?

The Lotto 6/42 is a popular lottery game in the Philippines organized by the Philippine Charity Sweepstakes Office (PCSO). In this game, players choose six numbers from a pool of 42 numbers.

To calculate the chances of winning the Superlotto 6/42, we need to determine the number of possible combinations and use the formula:

Odds of winning = 1 / (number of possible combinations)

To find the number of possible combinations, we use the concept of binomial coefficients. In this case, we need to calculate “42 choose 6” or the number of ways to choose 6 numbers out of 42.

The formula for binomial coefficients is:

nCr = n! / (r! * (n-r)!)

where n is the total number of items to choose from, and r is the number of items to choose.

For the Superlotto 6/42, the calculation would be:

42C6 = 42! / (6! * (42-6)!)

Simplifying the equation:

42C6 = 42! / (6! * 36!)

42! (42 factorial) means multiplying all the numbers from 42 down to 1:

42! = 42 * 41 * 40 * … * 1

6! (6 factorial) means multiplying all the numbers from 6 down to 1:

6! = 6 * 5 * 4 * 3 * 2 * 1

36! (36 factorial) means multiplying all the numbers from 36 down to 1:

36! = 36 * 35 * 34 * … * 1

Plugging these values into the equation:

42C6 = (42 * 41 * 40 * … * 1) / ((6 * 5 * 4 * 3 * 2 * 1) * (36 * 35 * 34 * … * 1))

Using a calculator or computer software, the calculation would result in:

42C6 = 5,245,786

Therefore, the number of possible combinations or tickets in the Superlotto 6/42 is 5,245,786.

Finally, to determine the odds of winning, we use the formula:

Odds of winning = 1 / (number of possible combinations)

Odds of winning = 1 / 5,245,786

This means that the chances of winning the Superlotto 6/42 jackpot prize are approximately 1 in 5,245,786.

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