Contents
- 1 How many ways can we distribute n balls among K bags?
- 2 What is the number of permutations of n balls formula?
- 3 How do you divide n identical things among r people?
- 4 How many ways can you arrange colored balls?
- 5 How many ways can group N objects be?
- 6 How to calculate the number of balls in a K box?
- 7 How many possible prize distributions are there at discount al’s?
How many ways can we distribute n balls among K bags?
If we are supposed to distribute k distinct objects to n identical recipients so that each gets at most one, we cannot do so if k>n, so there are 0 ways to do so. On the other hand, if k≤n, then it doesn’t matter which recipient gets which object, so there is only one way to do so.
What is the number of permutations of n balls formula?
Permutations & Combinations: Important Formulas
| Number of permutation of these N balls = | N! |
|---|---|
| (B1)! × (B2)! × (B3)! × – – – – – (Br)! |
How many ways there are to put n indistinguishable balls into k distinguishable bins?
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. There is no simple closed formula for this number.
How many balls boxes can contain?
No box can contain more than one ball or any box may contain more than one ball. 4. No box can be empty or any box can be empty.
How do you divide n identical things among r people?
For n distinct objects into r distinct groups:
- Number of ways exactly 1 object can be placed in r groups = nCr.
- Number of remaining objects = (n-r)
- Now, each of these (n-r) objects can be placed into any of the r groups.
- Hence, number of ways of distributing them = (n-r)^r.
How many ways can you arrange colored balls?
Answer: We can arrange 4 different colored balls in 24 ways.
How many ways are there to put 6 indistinguishable balls into 4 distinguishable boxes?
This answer is S(6,4), a Stirling number of the second kind. Since each box contains an object, there are 2 cases to consider: 1) If there is a 3/1/1/1 distribution, then there are (63)=20 possibilities (since the boxes are identical).
How many ways can 7 different balls?
100. In how many ways can 7 different balls be distributed in 5 different boxes if box 3 and box 5 can contain only one and two number of balls respectively and rest of the boxes can contain any number of balls? Explanation: One ball for box 3 can be selected in 7C1 ways.
How many ways can group N objects be?
The total number of ways that the parts can be selected is 4×3×5×4 or 240 ways. Factorial Notation: the notation n! (read as, n factorial) means by definition the product: n!
How to calculate the number of balls in a K box?
Let x 1, x 2, …, x k be the numbers of balls placed in box 1, 2, …, k, respectively. Then you are asking for the number of solutions in positive integers of the equation There are many ways you can go about this.
How to distribute n objects in your distinct groups?
It is given that, Now replace every xi with yi + 1 for all 1 ≤ i ≤ R. Now all the y variaables are greater than or equal to zero. It now reduces to that standard multinomial equation whose solution is (N – R) + R – 1CR – 1 .
Is the distribution of objects into bins a distinct problem?
A distribution of objects into bins is an arrangement of those objects such that each object is placed into one of the bins. In this type of problem, the objects and bins are distinct.
How many possible prize distributions are there at discount al’s?
There are 3 prizes that can be won: a 100 cm HDTV, a signed football jersey, and an envelope filled with gift cards. It is possible for a person to win more than one prize. How many possible prize distributions are there? Discount Al’s Thrift Shop is having a one-day going-out-of-business sale in which everything must go!