logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Permutations and Combinations
0 votes

Four couples (husband and wife) decide to form a committee of four members.The number of different committees that can be formed in which no couple finds a place is

$\begin{array}{1 1}(A)\;10\\(B)\;12\\(C)\;14\\(D)\;16\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
The number of committees of 4 gentlemen =$4C_4$
$\Rightarrow 1$
The number of committees of 3 gentlemen,1 wife =$4C_3\times 1C_1$
(After selecting 3 gentlemen only 1 wife is left who can be included)
The number of committees of 2 gentlemen 2 wives =$4C_2\times 2C_2$
The number of committees of 1 gentlemen 3 wives =$4C_1\times 3C_3$
The number of committees of 4 wives =1
$\therefore$ The required number of committees =1+4+6+4+1
$\Rightarrow 16$
Hence (D) is the correct answer.
answered May 19, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...