Permutations & Combinations
Arrangement in boxes with restrictions
nta_pyq_2025_apr
Grade 12
Question:
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:
$5880$
$960$
$840$
$5760$
Step-by-Step Solution
Key Concept: Model the box placement as arrangements with$adjacency/order$restrictions and use complementary counting if needed.
$(4)$= Total - [$(Allin1 and$$R_{3}$$)$+$( All i_n$$R_{2}$$and$$R_{3}$$)$+$( All i_n$$R_{1}$$and$$R_{2}$$)$] 8$6 = C_{5}$$\cdot$∣$5 - {5$+ ⌊$5 + C$5$\cdot 5}$– – = ⌊5($56 - 1 - 1 - 6) = 120$(48)$= 5760$
Correct Answer: 4