How many ways are there to put 4 distinguishable balls into 3 indistinguishable boxes?
How many ways are there to put 4 distinguishable balls into 3 indistinguishable boxes?
This gives us a total of- 1 + 3 + 4 + 6 = 14 ways. Example 2 – How many ways are there to put 4 indistinguishable balls into 3 indistinguishable boxes?
How many ways there are to put n indistinguishable balls into k distinguishable bins?
9
So the answer is 9. Distributing n indistinguishable objects into k indistinguishable boxes is the same as writing n as a sum of at most k positive integers in non-increasing order.
How many ways are there to put 6 indistinguishable balls into 4 distinguishable boxes?
=(64)⋅3=45 possibilities. Therefore there are 20+45=65 possible ways to do this.
How many ways can you distribute N distinguishable balls into P indistinguishable boxes?
The answer is always 1, because there’s only one way to put N balls into one box. When a combinatorics problem frames a question in terms of objects in boxes, it implies that the order of the objects inside the box does not matter.
How many ways are there to distribute 5 distinguishable balls into 4 distinguishable boxes so that no box is empty?
=24, for a total of 240. Your first part is correct.
How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are?
Each ball can be put into any one of the 3 boxes, independently of where the other balls are. There are 3*3*3*3 = 81 ways of doing this. There is no restriction of putting the balls in the boxes despite mentioning that there are 4 distinct balls and 3 distinct boxes.
How many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
ways. 10,395 is the number of ways to place2 each of 12 distinguishable balls in 6 indistinguishable bins, So 10,395×6! =7,484,400, the desired answer.
How many ways are there to distribute 6 objects into 5 boxes?
1 Approved Answer So, the total number of ways to place 5 distinct objects in 6 distinct boxes is 6*6*6*6*6 = 6^5 = 7776 Hence, there are 7776 ways to place five objects in six boxes when both are labeled.
How many ways are there to distribute 12 distinguishable balls into six distinguishable bins?
10,395 is the number of ways to place2 each of 12 distinguishable balls in 6 indistinguishable bins, So 10,395×6!
How many ways are there to place 8 indistinguishable balls in 4 distinguishable bins?
How many ways are there to place 8 indistinguishable balls into 4 distinguishable bins? = 11!/(8!
How many ways are there to place 10 distinguishable objects into 8 distinguishable boxes?
19,448 ways
Example: How many ways are there to place 10 indistinguishable balls into 8 distinguishable bins? Solution: We have C(10 + 8 – 1, 10) = C(17, 10) = 19,448 ways to arrange 10 indistinguishable balls into 8 distinguishable bins.
How to find out how the balls are distributed in boxes?
To find out how the balls are distributed in the boxes we use N − 1 “|”. That way we have M + N − 1 symbols If the boxes and balls were distinguishable we would have ( M + N − 1)! combinations. Since they are distinguishable we have to divide this by ( N − 1)! ⋅ M! . Example: M = 3 and N = 2 Could someone maybe explain this in more detail?
How many balls are there in the box?
There are 3 boxes (red, green, blue) and 7 distinguishable balls (two red balls, three blue balls, and two green balls). a. Find the number of ways to put the balls into the boxes with no restrictions.
What is indindistinguished boxes?
Indistinguishable boxes, then, implies that the order of the boxes themselves are not taken into account. If this is what you want, then the binomial coefficient
How do you identify a partition of balls in a box?
The answer is that each distribution of balls in boxes in the original question can be identified with a partition of the balls when they are arranged in a line. For example, if I have 3 boxes and 7 identical balls, I could place the 7 balls in a line like so:
