The problem can be solved using the concept of distribution of objects in combinatorics.

Step 1: Since each child must get at least one toy, we first distribute one toy to each child. There are 5 toys and 3 children, so this can be done in 5P3 = 5*4*3 = 60 ways.

Step 2: Now we have 2 toys left and 3 children. This is a problem of distributing n identical items (toys) among r persons (children), which can be done in (n+r-1)C(r-1) ways. Here, n=2 and r=3, so the number of ways = 4C2 = 6.

Step 3: Multiply the number of ways in step 1 and step 2 to get the total number of ways. So, 60*6 = 360.

So, the total number of ways in which 5 different toys can be distributed among 3 children such that each child gets at least one toy is 360.

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The problem can be solved using the concept of distribution of objects in combinatorics.

Step 1: Since each child must get at least one toy, we first distribute one toy to each child. There are 5 toys and 3 children, so this can be done in 5P3 = 5*4*3 = 60 ways.

Step 2: Now we have 2 toys left and 3 children. This is a problem of distributing n identical items (toys) among r persons (children), which can be done in (n+r-1)C(r-1) ways. Here, n=2 and r=3, so the number of ways = 4C2 = 6.

Step 3: Multiply the number of ways in step 1 and step 2 to get the total number of ways. So, 60*6 = 360.

So, the total number of ways in which 5 different toys can be distributed among 3 children such that each child gets at least one toy is 360.

Knowee AI · Accepted Answer

The problem can be solved using the concept of distribution of objects in combinatorics.

Step 1: Since each child must get at least one toy, we first distribute one toy to each child. There are 5 toys and 3 children, so this can be done in 5P3 = 5*4*3 = 60 ways.

Step 2: Now we have 2 toys left and 3 children. This is a problem of distributing n identical items (toys) among r persons (children), which can be done in (n+r-1)C(r-1) ways. Here, n=2 and r=3, so the number of ways = 4C2 = 6.

Step 3: Multiply the number of ways in step 1 and step 2 to get the total number of ways. So, 60*6 = 360.

So, the total number of ways in which 5 different toys can be distributed among 3 children such that each child gets at least one toy is 360.

5 different toys are to be distributed among 3 children such that any child gets at least 1 toy. What is the total number of ways in which it can be done ?120125130150

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