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.
How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable but the boxes are?
As there are 5 balls and three boxes each ball has 3 choices. So to answer is 3x3x3x3x3=243.
How many ways can you put 3 balls in 4 boxes?
Answer. If the balls are different, then there are 43 ways to put them in 4 boxes.
How many ways can you put 3 balls in 3 boxes?
meaning : 2 balls are in the left box, one ball is in the center box and one box is empty. Thus, to count all ways I took (52)=10. But answer is 33.
How many ways are there to put 4 distinguishable balls into 2 indistinguishable boxes?
So, we have 1+4+6+4+1=16 ways to distribute the balls but since the boxes are indistinguishable we must divide by 2! (or just 2) to eliminate redundancy. So, 8 ways of arranging the balls in groups.
How many ways are there to put 4 indistinguishable balls into 2 indistinguishable boxes?
Therefore, the number of ways of distributing 4 identical balls among 4 different boxes is: 1+12+18+4 = 35 ways. On the other hand, if the balls are different, each one may be placed in one of the 4 different boxes, so the number of ways in which this can be done with distinguishable outcomes is: 4^4 = 256 ways.
How many ways are there to put 4 distinguishable balls into 3 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 to put 4 indistinguishable balls into 2 distinguishable boxes?
How many ways are there to put the balls into the boxes?
How many ways are there to place the balls into the boxes? There are only six ways.
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.
