P & C Ques..pls hlp

[Tushar Mittal]

no of ways in which 3 diff children can pick up 5 diff toffees..?

is it same as distributing 5 different toffees to 3 different children? 

[Ravisankar Vemuri]

Hi Tushar,

no. of ways of distributing 5 diferent chocolates to three children:

the different ways are like this:

Two simulataneous calculations are required here. First one is about  how many chocolates - to whom? And the second calculation  is about which clocolates - to whom? 

5,0,0 set  -  (3!/2!)*(5!/5!) = 3

4,1,0 set - 3! * (5!/4!) = 30 ways 

3,2,0 set - 3! * (5!/3!2!) = 60 ways  

3,1,1 set - (3!/2!) * (5!/3!1!1!) = 60 ways  

2,2,1 set - (3!/2!) * (5!/2!2!)= 90 ways  

total = 243 ways

short cut:

"m different things can be distributed to n people in n^m ways"

5 different chocolates can be distributed to 3 children in 3^5 = 243 ways