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GATE Overflow | Mathematics | Test 1 | Question: 2

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Four couples 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?      

  1. 10
  2. 12
  3. 14
  4. 16
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Let the four couples be (assuming heterosexual peeps :P)

$M_1F_1,$  $M_2F_2,$  $M_3F_3,$  $M_4F_4$

 

If $M_1$ is chosen, $F_1$ must not be chosen and vice versa.

This is true for all the couples.

 

So, select exactly one member from each couple.

=> $_{1}^{2}\textrm{C}*_{1}^{2}\textrm{C}*_{1}^{2}\textrm{C}*_{1}^{2}\textrm{C}=16$

 

Option D

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