In a beg with 8 red balls and 11 blues balls how
many 5 balls boxes can be chosen those have 4
blue balls?
In a beg with 8 red balls and 11 blues balls how
many 5 balls boxes can be chosen those have 4
blue balls?
If the box has 4 blue balls, then that means the one remaining ball is red.
So, there is only one way to have a 5-ball box with 4 blue balls: It must have one red and 4 blues.
That is if all the balls of a color are identical. If they are somehow distinguishable, then there are
8 ways to choose the red ball
11C4 = 330 ways to choose the blue balls.
That would make 2640 ways to fill a 5-ball box with one red and 4 blue balls.
To find out how many 5-ball boxes can be chosen that have 4 blue balls, we can use combinations. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items we are choosing.
In this case, we have 11 blue balls and we want to choose 4 of them. So the formula becomes 11C4 = 11! / (4! * (11-4)!).
Now, let's calculate it step by step:
1. Calculate the factorial of 11:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800
2. Calculate the factorial of 4:
4! = 4 * 3 * 2 * 1 = 24
3. Calculate the factorial of (11-4):
(11-4)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
4. Substitute these values in the formula:
11C4 = 39,916,800 / (24 * 5,040) = 39,916,800 / 120 = 332,640
Therefore, there are 332,640 5-ball boxes that can be chosen with 4 blue balls from a bag containing 8 red balls and 11 blue balls.