Question

Find number of ways of distributing 8 different items equally among two children.
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In how many ways can five people be divided into three groups?​

Answer 1

Answer:

16, 54

Step-by-step explanation:

Each child should get items equally,

So each child shall get 4 items.

No. of ways 4 items can be given to one child =

4P1 = 4 ways

Similarly there are 4 ways for second child

Hence, 8 items distributed equally among 2 children would be done in 4 × 4 = 16 ways.

Number of ways 5 people can take 3 places (groups) = 5P3 = 60

But this includes groups in which there are 0 people, so we will need to remove those cases.

Subtracting cases where only first, second or third group is empty = 60 - 3 = 57

Subtracting cases where 1st and 2nd, 1st and 3rd, 2nd and 3rd groups are empty simultaneously = 57 - 3 = 54