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

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The equation 9!/(9 - r)! = 840 was analyzed to find the correct value of r. Initially, r was thought to be 4, but upon recalculating, it was determined that 9!/(5!) equals 3024, not 840. Consequently, there is no integer solution for r within the range of 0 to 9 that satisfies the equation. The discussion highlights the importance of careful calculation in solving factorial equations. Ultimately, the conclusion is that the equation has no valid solution.
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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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