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Question: Answered & Verified by Expert
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?
MathematicsPermutation CombinationNDANDA 2011 (Phase 1)
Options:
  • A $m>n$
  • B $m=n$
  • C $m=n-1$
  • D $m=n-2$
Solution:
2052 Upvotes Verified Answer
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 $=n={ }^{9} C_{5}$
$\Rightarrow n=126$
$\Rightarrow m=n$

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