Let A = x_1 , , x_2 , ,............, x_7 and B = y_1 , , y_2 , , … - Vidyadip

MCQ

Let $A = \{ {x_1},\,{x_2},\,............,{x_7}\} $ and $B = \{ {y_1},\,{y_2},\,{y_3}\} $ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f : A \to B$ that are onto, if there exist exactly three elements $x$ in $A$ such that $f(x)\, = y_2$, is equal to

✓
$14.{}^7{C_3}$
B
$16.{}^7{C_3}$
C
$14.{}^7{C_2}$
D
$12.{}^7{C_2}$

✓

Answer

Correct option: A.

$14.{}^7{C_3}$

a
Number of onto function such that exactly three elements in $x \in A$ such that $f\left( x \right) = \frac{1}{2}$ is

equal to $ = {\,^7}{C_3},\left\{ {{2^4} - 2} \right\} = 14.{\,^7}{C_3}$

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