Question

Calculate the number of ways which 12 distinct candies can be divided among 2 children in a way that the first child gets 5 candies and the second gets 7 candies​

Answer 1

Given : 12 distinct candies  be divided among 2 children in a way that the first child gets 5 candies and the second gets 7 candies​

To Find  :   number of ways  

Solution:

Either we can select 5 candies for a child   or 7 candies for a child

Each can be selected in ¹²C₅ or ¹²C₇  ways   ( if one is selected , other is automatically selected as total are 12 candies only )

Then we can select one child to give either  5 or 7 candies

Hence total Ways = 2 *  ¹²C₅   =  2 *  ¹²C₇  

= 2 *  42

= 84

in 84 ways  12 distinct candies can be divided among 2 children in a way that the first child gets 5 candies and the second gets 7 candies​

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Answer 2

Answer:

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