Question
Quantitative Aptitude Question on Permutations and Combinations
How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?
A
4
B
3
C
2
D
6
Answer
6
Explanation
Solution
Here order is important, therefore, we'll use Perm.
All the possible ways in which 2 stud can be seated on 4 seats = 4P2.
Suppose, two students are always seated together. Then we'll treat them as 1 stud & the seats left to be filled are 3. Therefore no. of ways in which 2 stud are always seated together = 3P2.
Now, the no. of ways in which 2 students have a gap in between = total no. of ways - no. of ways in which students are seated together = 4P2-3P2 = 12-6 = 6
The correct option is (D): 6