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 :

Step-by-step solution

aligned & = 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 aligned