In a lottery game, a player picks 7 numbers from 1 to 47. How many different choices does the player have if order doesn't matter?
47C7 = 62891499
You are choosing 7 from 47, that is called
C(47,7)
= 47!/(7! 40!)
My calculator has the nCr button and gave me 62,891,499
if not, then
47!/(7! 40!)
= 47*46*45*44*43*42*41*40*39*...*1 / ((40*39*....1)(7*6*5*4*3*2*1))
= 47*46*45*44*43*42*41 / (7*6*5*4*3*2*1)
= 62,891,499
Well, let me put it this way. Picking 7 numbers out of 47 is like trying to find a needle in a haystack, but with more numbers and less straw. With so many possibilities, it's like playing hide-and-seek in a stadium with 47 different hiding spots. Now, let's do some math. Since order doesn't matter, you're essentially choosing a group of 7 numbers from a set of 47. So, using some fancy combinatorics, we can calculate that there are 47 choose 7 different choices for the player. That means there are approximately 62,891,499 different ways to pick 7 numbers out of 47. Good luck finding the winning combination!
To find the number of different choices the player has if order doesn't matter, we can use the concept of combinations.
In this case, we need to choose 7 numbers out of a set of 47 numbers without regard to their order. The formula for combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where:
- n is the total number of items in the set (47 in this case)
- r is the number of items we want to choose (7 in this case)
- ! denotes factorial, which means multiplying a number by all positive whole numbers less than itself down to 1.
Now, let's calculate the number of different choices:
C(47, 7) = 47! / (7! * (47-7)!)
Cancelling out terms:
C(47, 7) = (47 * 46 * 45 * 44 * 43 * 42 * 41) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
Now, let's calculate the value using a calculator or computational tool:
C(47, 7) ≈ 62,891,146
Therefore, the player has approximately 62,891,146 different choices if order doesn't matter.
To determine the number of different choices the player has if order doesn't matter, we can use the concept of combinations.
In this case, we can use the formula for combinations to find the answer. The formula for combinations is:
C(n, r) = n! / (r!(n - r)!)
Where n represents the total number of items to choose from and r represents the number of items to choose.
In the given scenario, the player picks 7 numbers from 1 to 47, so n = 47 and r = 7. Substituting these values into the formula, we have:
C(47, 7) = 47! / (7!(47 - 7)!)
Now, let's calculate:
47! = 47 × 46 × 45 × ... × 2 × 1
7! = 7 × 6 × 5 × ... × 2 × 1
40! = 40 × 39 × 38 × ... × 2 × 1
After simplification, the formula becomes:
C(47, 7) = (47 × 46 × 45 × ... × 40) / (7 × 6 × 5 × ... × 2 × 1)
Calculating the numerator:
47 × 46 × 45 × ... × 40 = 34,358,232,720
Calculating the denominator:
7 × 6 × 5 × ... × 2 × 1 = 5,040
Now we can divide the numerator by the denominator:
C(47, 7) = 34,358,232,720 / 5,040
C(47, 7) ≈ 6,834,808
Therefore, the player has approximately 6,834,808 different choices if order doesn't matter.