Question 40 of 278MediumMCQ
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
Solutions · 1
Official solution
\[3 \text { Shelf empty: }(8,0,0,0) \rightarrow 1 \text { way }\]
\[\left.2 \text { shelf empty: } \[\begin{gathered} (7,1,0,0) \\ (6,2,0,0) \\ (5,3,0,0) \\ (4,4,0,0) \end{gathered}\]\right] \rightarrow 4 \text { ways }\]
\[\left.1 \text { shelf empty: } \[(6,1,1,0)(4,2,1,0)(4,3,0)(3,3,2,0)(4,2,2,0)\]\right] \rightarrow 5 \text { ways }\]
\[\left.0 \text { Shelf empty : } \[(1,2,3,2)(2,2,2,2)(3,3,2,1,1)(4,2,1,1)(5,1,1,1)\]\right] \rightarrow 5 \text { ways }\]
Total =15 ways Answer the question to unlock