+1 vote
in JEE by kratos

If 2 boys and 2 are to be arranged in a row so that the are not next to each other,how many possible arrangements are there?

(a) 3

(b) 6

(c) 12

(d) 24

1 Answer

+6 votes
by kratos
 
Best answer

Correct option (c) 12

Explanation:

2 boys and 2 are to be arranged in a row so that the are not next to each other. Hence, they must sit alternatively. Let us place the boys first:

We can place these boys in 2! = 2 ways

Now, as we can see in the above arrangement, there are three places to choose from in order to place 2 *****

Number of ways we can choose 2 places out of 3 = 3C2 = 3C1 = 3

Also, the ***** can interchange their positions in 2! = 2 ways.

Hence, total number of possible arrangements = 2 × (3 × 2) = 12

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