Table of Contents
- 1 How many ways are there to place 10 indistinguishable balls into 8 distinguishable bins?
- 2 How many ways are there to put 4 indistinguishable balls into 3 indistinguishable boxes?
- 3 How many ways are there to put 10 numbered balls into 4 numbered boxes a box is allowed to be empty )?
- 4 How many ways can you put 5 balls in 3 boxes?
- 5 Where should I place the balls in the box?
How many ways are there to place 10 indistinguishable balls into 8 distinguishable bins?
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 many ways are there to distribute 10 distinct objects into 4 distinct boxes?
A simple modification to the above code shows that there are 168 ways to distribute 10 identical balls into 4 distinct boxes such that no box contains exactly 3 balls: Looks like Stev Iones has the right answer: 334,816 ways.
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 put 4 indistinguishable balls into 3 indistinguishable boxes?
Indistinguishable balls and Indistinguishable boxes – Example 1 – How many ways are there to put four different balls into three indistinguishable offices without exclusion? This gives us a total of- 1 + 3 + 4 + 6 = 14 ways.
How many ways are there of placing 6 indistinguishable packages in 10 shipping boxes?
Thus, we have 1*1+3*3+3*6=28 total possibilities.
How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?
evaluating the number of ways to distribute six indistinguishable balls into nine distinguishable bins, we can use the combination formula. This is because order is not important and repetition is allowed. The combination formula is C(n+r−1,r). =14!/6!(
How many ways are there to put 10 numbered balls into 4 numbered boxes a box is allowed to be empty )?
Applying multiplication principle then, there are (42)(210−2)=6132 ways to arrange the ten balls among the four boxes having exactly two boxes empty.
How many ways can you distribute 6 balls into distinct 5 boxes?
The number of ways by which 6 distinct balls can be put in 5 distinct boxes are
- 7776.
- 15625.
- 720.
- 120.
How many ways to distribute 5 balls into 3 boxes if each box must have at least one ball in it if?
We have to distribute 5 distinct balls into 3 identical boxes. Thus, n = 5 and k = 3. Therefore, there are a total of 41 possibilities.
How many ways can you put 5 balls in 3 boxes?
So, the number of ways you can put 5 balls in 3 boxes is 21.
How many distinct balls are put into nine indistinguishable boxes?
Ten distinct balls are put into nine indistinguishable boxes so that no box is empty. What is the number of ways of placing these balls? Quartile PPC ads management solution. Certified PPC ad solution to help manage, forecast, optimize e-commerce campaigns.
How many balls can you put in a box?
There are ( 10 2) ways to select 2 balls from the set of 10 distinct balls to put them in one box, and the rest of the boxes will take 1 ball each. Since boxes are indistinguishable, the number of ways in which ten distinct balls are put into nine boxes so that no box is empty is the same i.e. ( 10 2).
Where should I place the balls in the box?
When you place the ball 1 in the leftmost box, you can still put ball 2 in any box. But, if you put ball 1 in the rightmost box, all 5 balls need to be in the rightmost box. You should be able to work through the resulting combinations.