Number of ways, in which letters A, B, C, D, E can be placed in 8 boxes of figure below so that no r

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6.Permutation and Combination

hard

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 :

A$5880$

B$960$

C$840$

D$5760$

(JEE MAIN-2025)

Solution

image
$=$ Total $-\left[\left(\right.\right.$ All in $R _1$ and $\left.R _3\right)+\left(\right.$ All in $R _2$ and $\left.R _3\right)+$ (All in $R_1$ and $R_2$ )]
$={ }^8 C _5 \cdot \underline{5}-\left\{\left\lfloor 5+\left\lfloor 5+{ }^6 C _5 \cdot \underline{\mid}\right\}\right.\right.$
$=\lfloor 5(56-1-1-6)=120(48)$
$=5760$

Standard 11

Mathematics

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(JEE MAIN-2021)

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 :

Solution

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