What is the Correct Value of r if 9!/(9-r)! = 840?

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SUMMARY

The equation 9!/(9 - r)! = 840 has no integer solutions for r within the range of 0 to 9. The initial assumption that r equals 4 is incorrect, as substituting this value results in 3024, not 840. The correct approach involves recognizing that the factorial division does not yield the target value for any integer r in the specified range.

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9!/(9 - r)! = 840

I found r to be 4.

Is this correct?
 
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RTCNTC said:
9!/(9 - r)! = 840

I found r to be 4.

Is this correct?

$\dfrac{9!}{(9-4)!} = \dfrac{9!}{5!} = 9 \cdot 8 \cdot 7 \cdot 6 = 3024$

there is no solution to the equation $\dfrac{9!}{(9-r)!} = 840$ for $0 \le r \le 9 \, , \, r \in \mathbb{Z}$
 
I messed up in my calculation. Thanks.
 

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