SATHEE: Permutations And Combinations Question 328

Permutations And Combinations Question 328

There are 10 bags $ B_1,B_2,B_3,…,B_{10}, $ which contain 21, 22, …, 30 different articles respectively. The total number of ways to bring out 10 articles from a bag is

Options:

A) $ ^{31}C _{20}{{-}^{21}}C _{10} $

B) $ ^{31}C _{17} $

C) $ ^{31}C _{11} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

[a] The required number of ways $ {{=}^{21}}C _{10}{{+}^{22}}C _{10}{{+}^{23}}C _{10}+…{{+}^{30}}C _{10} $ $ ={{(}^{21}}C _{10}{{+}^{21}}C _{11}{{+}^{22}}C _{12}{{+}^{23}}C _{13}+…{{+}^{30}}C _{20}){{-}^{21}}C _{11} $ $ {{=}^{22}}C _{11}{{+}^{22}}C _{12}{{+}^{23}}C _{13}+…{{+}^{30}}C _{20}{{-}^{21}}C _{10} $ $ ({{\because }^{n}}{C _{r-1}}{{+}^{n}}C _{r}{{=}^{n+1}}C _{r}) $ $ {{=}^{31}}C _{20}{{-}^{21}}C _{10}. $

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Permutations And Combinations Question 328

There are 10 bags $ B_1,B_2,B_3,…,B_{10}, $ which contain 21, 22, …, 30 different articles respectively. The total number of ways to bring out 10 articles from a bag is

Options:

Answer:

Solution:

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