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5 books are to be chosen from a lot of 10 books. If $m$ is the number of ways of choice when one specified book is always included and $n$ is the number of ways of choice when a specified book is always excluded, then which one of the following is correct?
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The correct answer is:
$m=n$
Number of ways when one specified book is always included. So, 4 books can be chosen from remaining 9 ways:
$=m={ }^{9} C_{4}$
$\Rightarrow m=126$
and number of ways when one specified book is always excluded $=n={ }^{9} C_{5}$
$\Rightarrow n=126$
$\Rightarrow m=n$
$=m={ }^{9} C_{4}$
$\Rightarrow m=126$
and number of ways when one specified book is always excluded $=n={ }^{9} C_{5}$
$\Rightarrow n=126$
$\Rightarrow m=n$
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