Permutations And Combinations Question 135

Question: In how many ways can 6 persons be selected from 4 officers and 8 constables, if at least one officer is to be included [Roorkee 1985; MP PET 2001]

Options:

A) 224

B) 672

C) 896

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • Required number of ways $ {{=}^{4}}C_1{{\times }^{8}}C_5{{+}^{4}}C_2{{\times }^{8}}C_4{{+}^{4}}C_3{{\times }^{8}}C_3{{+}^{4}}C_4{{\times }^{8}}C_2 $ $ =4\times 56+6\times 70+4\times 56+1\times 28=896 $ .

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