Question

If $A=\{8,9,10\}$ and $B=\{1,2,3,4,5\}$, then the number of elements in $A\times A\times B$are

• A. $15$
• B. $30$
• C. $45$
• D. $75$

Answer 1

The correct option is C

$45$

Explanation for correct option:

Finding the number of elements:

Given, $A=\{8,9,10\}$ & $B=\{1,2,3,4,5\}$

Number of element present in $A,n\left(A\right)=3$

Number of element present in$B,n\left(B\right)=5$

Number of element present in,

$\begin{array}{rcl}A\times A& =& n\left(A\right)\times n\left(A\right)\\ & =& 3\times 3\\ & =& 9\end{array}$

Number of element present in,

$\begin{array}{rcl}A\times A\times B& =& n\left(A\right)\times n\left(A\right)\times n\left(B\right)\\ & =& 9\times 5\\ & =& 45\end{array}$

Hence, the correct option is $\left(C\right)$.