Solve the following

Question:

If nPr = 840 and nCr = 35, then r = ___________.

Solution:

Given  nPr = 840 and nCr = 35

i. e $\frac{n !}{(n-r) !}=840$ and $\frac{n !}{r !(n-r) !}=35$

$\therefore\left(\frac{n !}{(n-r) !}\right) \frac{1}{r !}=35$

i. e $840\left(\frac{1}{r !}\right)=35 \quad\left(\because \frac{n !}{(n-r) !}=840\right.$ given $)$

i. e $r !=\frac{840}{35}=24$

$=4 \times 3 \times 2$

$=4 !$

i.e $r=4$

 

 

 

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