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 :

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 :

TestHub · Accepted Answer

​ = Total − [ ( All in 1 ​ and R 3 ​ ) + ( All in R 2 ​ and R 3 ​ ) + ( All in R 1 ​ and R 2 ​ ) ] = 8 C 5 ​ ⋅ ∣ 5 − { 5 ​ + ⌊ 5 + 6 C 5 ​ ⋅ 5 ​ } = ⌊ 5 ( 56 − 1 − 1 − 6 ) = 120 ( 48 ) = 5760 ​

Mathematics - Permutation & Combination Question with Solution | TestHub

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