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JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 2 April · Evening Shift · Mathematics · Permutation and Combination

The number of ways, in which the letters A, B, C , D, E can be...

The number of ways, in which the letters A,B,C\mathrm{A}, \mathrm{B}, \mathrm{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 :
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

Options

  1. A58805880
  2. B960960
  3. C840840
  4. D57605760

Correct answer

D. 57605760

Step-by-step solution

= Total −[(Allin1 and  R3)+( All in R2 and R3)+( All in R1 and R2)]=8C5⋅∣5−{5‾+⌊5+6C5⋅5‾}=⌊5(56−1−1−6)=120(48)=5760\begin{aligned} & =\text{ Total }-\left[\left(\mathrm{All} \mathrm{in}_1 \text{\text{ and } } \mathrm{R}_3\right)+\left(\text{ All in } \mathrm{R}_2 \text{ and } \mathrm{R}_3\right)+\right. \\ & \left.\left(\text{ All in } \mathrm{R}_1 \text{ and } \mathrm{R}_2\right)\right] \\ & ={ }^8 \mathrm{C}_5 \cdot \mid 5-\left\{\underline{5}+\left\lfloor 5+{ }^6 \mathrm{C}_5 \cdot \underline{5}\right\}\right. \\ & =\lfloor 5(56-1-1-6)=120(48) \\ & =5760\end{aligned}
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