the number of ways of distribution 10 different awards to 4 actors such that 2 actors may get 2 awards each and the rest 2 actors gets 3 awards each
Answers
Answer:
Step-by-step explanation:
Given : distribution of 10 different awards to 4 actors such that 2 actors may get 2 awards each and the rest 2 actors gets 3 awards each
To Find : number of ways
Solution:
Awards can be distributed in following ways
we need to distribute awards 2 , 2 , 3 , 3 groups
persons can be selected for 2 awards or 3 award in
⁴C₂ = 6 ways of 4!/2!.2! = 6 Ways
Awards can be distributed in
= ¹⁰C₂.⁸C₂.⁶C₃.³C₃
= 45 . 28 . 20 . 1
= 25200
or
= ¹⁰C₃.⁷C₃.⁴C₂.²C₂
= 120 . 35 . 6 . 1
= 25200
or
= ¹⁰C₃.⁷C₂.⁵C₃.²C₂
= 120 . 21 . 10 . 1
= 25200
or
= ¹⁰C₂.⁸C₃.⁵C₃.²C₂
= 45 . 56 . 10 . 1
= 25200
Total Possible combinations of ways = 6 x 25200
= 1,51,200
number of ways of distribution 10 different awards to 4 actors such that 2 actors may get 2 awards each and the rest 2 actors gets 3 awards each
= 1,51,200
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