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 × B. Then :

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 × B. Then : (A) y=273 x (B) 2 y=91 x (C) y=91 x (D) 2 y=273 x

Tardigrade Admin · Accepted Answer

x= 5 C3 × 3 !=60 y= 15 C3 × 3 !=15 × 14 × 13=30 × 91 ∴ 2 y=91 x

Q. 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 :

$y = 273 x$

$2 y = 91 x$

$y = 91 x$

$2 y = 273 x$

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

Q. 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×B. Then :

y=273x

2y=91x

y=91x

2y=273x