In the 6/50 lottery game, a player picks six numbers from 1 to 50. How many different choices does the player have?
Your answer is
To determine the number of different choices a player has in the 6/50 lottery game, we can use the concept of combinations.
In this case, we need to calculate the number of ways to choose 6 numbers out of a set of 50 numbers. This can be represented by the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items to choose from, and r is the number of items to choose.
In our case, n = 50 (as there are 50 numbers to choose from) and r = 6 (as the player needs to choose 6 numbers).
Applying the formula, we get:
C(50, 6) = 50! / (6! * (50 - 6)!)
Calculating the factorial terms:
50! = 50 * 49 * 48 * 47 * 46 * 45 * 44 * ... * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
44! = 44 * 43 * 42 * ... * 1
By simplifying the equation, we find:
C(50, 6) = (50 * 49 * 48 * 47 * 46 * 45) / (6 * 5 * 4 * 3 * 2 * 1)
Evaluating this expression will give us the answer.
To calculate the number of different choices the player has in a 6/50 lottery game, we can use the combination formula.
The formula to calculate the number of combinations is given by:
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)
In this case, the player picks six numbers from a pool of 50 numbers, so n = 50 and r = 6.
Plugging the values into the formula:
C(50, 6) = 50! / (6! * (50-6)!)
Now we can calculate the number of different choices:
C(50, 6) = 50! / (6! * 44!)
Using a calculator or programming tool with support for large factorials, we can compute this value as:
C(50, 6) = 15,890,700
Therefore, the player has 15,890,700 different choices in the 6/50 lottery game.