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  • Let <img alt="A=\left\{x_1, x_2, x_3, x_4, x_5, x_6\right\}, B=\left\{y_1, y_2, y_2, y_4, y_5, y_6\right\}" src="https://entrancecorner.oncodecogs.com/gif.latex?A%3D%5Cleft%5C%7Bx_1%2C%20x_2%2

Let A=\left\{x_1, x_2, x_3, x_4, x_5, x_6\right\}, B=\left\{y_1, y_2, y_2, y_4, y_5, y_6\right\}

Then the number of one-one mappings from A to B such that f\left(x_i\right) \neq y_i, i=1,2,3,4,5,6 is 

Option: 1

720

 


Option: 2

265


Option: 3

360

 


Option: 4

145


Answers (1)

best_answer

\because f\left(x_i\right) \neq y_i

i.e, no object goes to its scheduled place. Then number of one - one mappings

\begin{aligned} & =\left\lfloor 6\left(1-\frac{1}{L 1}+\frac{1}{L 2}-\frac{1}{L 3}+\frac{1}{L 4}-\frac{1}{L 5}+\frac{1}{L 6}\right)\right. \\ \\& =L 6\left(\frac{1}{L 2}-\frac{1}{L 3}+\frac{1}{L 4}-\frac{1}{L 5}+\frac{1}{L 6}\right) \\ \\& =360-120+30-6+1 \\ \\& =265 \end{aligned} 

Posted by

Kuldeep Maurya

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