What is the denominator of the reduced fraction representing the probability of winning Fantasy Five (a lottery game where the winner correctly chooses five numbered balls (without regard to order) from a group of 39 numbered balls)

Denominator = 69090840

Explanation:

In a Fantasy Five lottery game, we have to correctly guesses the five numbered balls to win the game.

So we have to select five balls, there are total 39 balls.

The probability of correctly selecting a ball is

P(ball) = 1/total no. of balls

The probability of correctly selecting 1st ball is

P(1st ball) = 1/39

Now there are 38 balls remaining

The probability of correctly selecting 2nd ball is

P(2nd ball) = 1/38

Now there are 37 balls remaining

The probability of correctly selecting 3rd ball is

P(3rd ball) = 1/37

Now there are 36 balls remaining

The probability of correctly selecting 4th ball is

P(4th ball) = 1/36

Now there are 35 balls remaining

The probability of correctly selecting 5th ball is

P(5th ball) = 1/35

The probability of selecting all 5 balls correctly is

P(5 balls) = P(1st ball)*P(2nd ball)*P(3rd ball)*P(4th ball)*P(5th ball)

P(5 balls) = 1/39*1/38*1/37*1/36*1/35

P(5 balls) = 1/69090840

Therefore, the denominator of the reduced fraction representing the probability of winning Fantasy Five lottery game is 69090840.