Permutation Combination Question 5
Question 5 - 2024 (29 Jan Shift 2)
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
(1) 18
(2) 16
(3) 12
(4) 15
Show Answer
Answer (4)
Solution
3 Shelf empty: $(8,0,0,0) \rightarrow 1$ way
2 shelf empty : $\left.\begin{array}{c}(7,1,0,0) \\ (6,2,0,0) \\ (5,3,0,0) \\ (4,4,0,0)\end{array}\right] \rightarrow 4$ ways
1 shelf empty : $\left.\begin{array}{rr}(6,1,1,0) & (3,3,2,0) \\ (4,2,1,0) & (4,2,2,0)\end{array}\right] \rightarrow$ 5ways
$(1,2,3,2) \quad(5,1,1,1)$
0 Shelf empty : $\left.\begin{array}{l}(2,2,2,2) \\ (3,3,1,1) \text \\ (4,2,1,1)\end{array}\right] \rightarrow$ 5ways
Total $=15$ ways
