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  • If n is an integer between 0 and 21 , then the minimum value of n !(21-n) ! is  Option: 1 <img alt="9 !

If n is an integer between 0 and 21 , then the minimum value of n !(21-n) ! is

 

Option: 1

9 ! 2 !
 


Option: 2

10 ! 11 !


Option: 3

20 !

 


Option: 4

21!


Answers (1)

best_answer

\begin{aligned} n !(21-n) ! & =21 ! \cdot \frac{n !(21-n) !}{21 !} \\ & =21 ! \cdot \frac{1}{{ }^{21} C_n}=\frac{21 !}{{ }^{21} C_n} \end{aligned}

For minimum value, { }^{21} C_n is maximum

Maximum value of { }^{21} C_n={ }^{21} C_{\frac{21-1}{2}}={ }^{21} C_{10}

\therefore Minimum value 

              =\frac{21 !}{{ }^{21} C_{10}}=\frac{21 !}{21 !} \times 10 ! 11 !=10 ! 11 !

Posted by

Rishi

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