1
The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : [figure]
- 5880
- 840
- 960
- 5760
Answer
(4) 5760
Solution
The rows contain 3, 3 and 2 boxes (total 8).
Ways to place 5 distinct letters in 8 boxes (one letter per box) = 8P5 = 8 7 6 5 4 = 6720
Subtract the cases in which a row is empty:
A row of 3 boxes empty: letters in the remaining 5 boxes = 5P5 = 120; two such rows 2 120 = 240
The row of 2 boxes empty: letters in the remaining 6 boxes = 6P5 = 720
Two rows empty leaves at most 3 boxes for 5 letters — impossible.
required number = 6720 - 240 - 720 = 5760
Answer: (4)
JEE Main 2025 (Online) 2nd April Evening Shift