Permutations And Combinations Question 136

Question: To fill 12 vacancies there are 25 candidates of which five are from scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made [RPET 1981]

Options:

A) $ ^{5}C_3{{\times }^{22}}C_9 $

B) $ ^{22}C_9{{-}^{5}}C_3 $

C) $ ^{22}C_3{{+}^{5}}C_3 $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • The selection can be made in $ ^{5}C_3{{\times }^{22}}C_9 $ . {Since 3 vacancies filled from 5 candidates in $ ^{5}C_3 $ ways and now remaining candidates are 22 and remaining seats are 9}.