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  • Let set 'A' has 7 elements and set B has 5 elements. If one function is selected from all possible defined functions from A to B then the probability that it is onto is<div class='qna-o

Let set 'A' has 7 elements and set B has 5 elements. If one function is selected from all possible defined functions from A to B then the probability that it is onto is

Option: 1

\frac{7!\times 2}{3\times 5^{6}}
 

 


Option: 2

\frac{7!}{10\times 5^{6}}


Option: 3

\frac{7!}{5^{6}}

 


Option: 4

\frac{7!}{5^{7}}


Answers (1)

best_answer

 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

 

 

- wherein

Where n repeated experiment and E occurs r times.

 

 

Total number of functions from A to B =n(s)=5^{7}

total number of onto finctions from A to B is

=n(E)=\frac{7!}{3!4!}\times 5!+\frac{7!}{3!2!}\times \frac{1}{2!2!}\times 5!=\frac{7!\times 20}{6}

\therefore P(E)=\frac{n(E)}{n(S)}=\frac{7!\times 2}{3\times 5^{6}}

Posted by

Gaurav

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