- In the State of Georgia, one of the most popular lottery games is called Mega Millions. To play Mega Millions, you pay $1 and try to pick the numbers that will match five white balls and the one mega ball. There are 56 white balls numbered 1 to 56; and 46 mega balls numbered 1 to 46. How many combinations of white and mega balls can be drawn? Note, the drawings are without replacement.
To calculate the number of combinations of white balls and mega balls that can be drawn in the Mega Millions lottery game, we need to use the concept of combinations.
In this case, we need to calculate the number of combinations of choosing 5 white balls out of 56 and 1 mega ball out of 46.
The formula for calculating the number of combinations is:
C(n, r) = n! / (r!(n - r)!)
Where:
- C(n, r) represents the number of combinations of n items taken r at a time
- n! represents the factorial of n, which is the product of all positive integers less than or equal to n
- r! represents the factorial of r
- (n - r)! represents the factorial of (n - r)
Using this formula, we can calculate the number of combinations for the white balls and mega balls:
C(56, 5) = 56! / (5!(56 - 5)!) = 56! / (5! * 51!)
Similarly,
C(46, 1) = 46! / (1!(46 - 1)!) = 46! / (1! * 45!)
Finally, to calculate the total number of combinations of white and mega balls that can be drawn, we multiply the number of white ball combinations with the number of mega ball combinations:
Total number of combinations = C(56, 5) * C(46, 1)
Now, you can use a calculator or a programming language that supports factorial calculations to calculate the values and multiply them together to find the total number of combinations.