If A = {1, 2, 3, 4, 5, 6}, Find the Number of Subsets Containing 2, 3 and 5
Question
If
\[ A=\{1,2,3,4,5,6\}, \]
then the number of subsets of \( A \) containing elements \( 2, 3 \) and \( 5 \) is ……………………….
Solution
The set \( A \) has:
\[ 6 \]
elements.
The subsets must contain:
\[ 2,\ 3,\ 5 \]
These three elements are fixed in every subset.
The remaining elements are:
\[ 1,\ 4,\ 6 \]
Each of these remaining \( 3 \) elements may either be included or not included independently.
Therefore, the number of required subsets is:
\[ 2^3=8 \]
Hence, the required answer is:
\[ \boxed{8} \]