Permutations & Combinations
Counting subsets with bounded cardinality
MMTS_Full_Test_16
Grade 12
Question:
Let $A=\{1,2,3,\ldots,10\}$, $B=\{4,8,12,16,20\}$ and $C=\{D:D\subseteq A,\,D\cap B\neq\emptyset\}$. The number of elements in $C$ which have at least 3 but at most 6 cardinal number is
Step-by-Step Solution
Key Concept: Count subsets $D$ of $A$ with $|D|\in\{3,4,5,6\}$ and $D\cap B\neq\emptyset$. Use complement: (all such subsets) $-$ (those with $D\cap B=\emptyset$).
Answer: 9036.
Correct Answer: 9036