Permutations And Combinations Question 140

Question: The number of ways in which 10 persons can go in two boats so that there may be 5 on each boat, supposing that two particular persons will not go in the same boat is [Pb. CET 1999]

Options:

A) $ \frac{1}{2}{{(}^{10}}C_5) $

B) $ 2{{(}^{8}}C_4) $

C) $ \frac{1}{2}{{(}^{8}}C_5) $

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • First omit two particular persons, remaining 8 persons may be 4 in each boat. This can be done in $ ^{8}C_4 $ ways. The two particular persons may be placed in two ways one in each boat. Therefore total number of ways are $ =2{{\times }^{8}}C_4 $ .