Question

Let $x$ denote the total number of one-one functions from a set A with 3 elements to a set $B$ with 5 elements and y denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then :

• A. $y=273 x$
• B. $2 y=91 x$
• C. $y=91 x$
• D. $2 y=273 x$

Answer 1

Answer: (B)

$x={ }^{5} C_{3} \times 3 !=60$
$y={ }^{15} C_{3} \times 3 !=15 \times 14 \times 13=30 \times 91$
$\therefore 2 y=91 x$