How do one know permutation or combination to be used in a question ?

Question

Suppose if we have

• 6 Different English movies
• 8 Different Malayalam Movies
• 10 Different Hindi Movie

How many ways we can choose 2 movies of different languages ?

How do one know Permutation or combination is to be used in a question ?

Answer 1

2 different languages movies.

Case 1. 1 english 1 malayalam

Case 2. 1 english 1 hindi

Case 3. 1 hindi 1 malayalam

Now see in what order we choose doesn't matter, i can choose 1 english movie out of the 6 first and then 1 malayalam movie out of 8 or 1 malayalam movie first and then choose english, both are same order doesnot matter.

Incases where order doesnt matter, it is COMBINATION, in case where order matters it is PERMUTATION.

So in this question, case 1 + case 2 + case 3 i.e 6C1 x 8C1 + 6C1 x 10C1 + 10C1 x 8C1 = 188

Answer 2

Method 1 : 

No. of choosing 2 movies from different  language  =  

       Total no of ways of choosing 2 movies  -  no of ways of choosing 2 movies from same language

 =  ²⁴C₂  - [ ⁶C₂  + ⁸C₂   + ¹⁰C₂]  = 188

Method 2: 

No. of choosing 2 movies from different  language  =  

= no. of ways of choosing[ (1  english movies & 1 hindi ) or (1  Malayalam movies & 1 hindi)  or (1  english movies & 1 Malayalam)

=  ⁶C₁  * ¹⁰C₁ + ⁸C₁  * ¹⁰C₁ +⁶C₁  * ⁸C₁    = 188

How do one know Permutation or combination is to be used in a question ?

Ans  : For this just practice,practice,practice.