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Class 11MathematicsPermutations and CombinationsPermutationsExpert
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In a row of (9) distinct people, how many arrangements have exactly (3) people between (P) and (Q)?

Answer and explanation

Correct answer: (60480)

There are (5) position pairs for (P) and (Q), with (2!) orders, and the remaining (7) people can be arranged in (7!) ways. Exam tip: count distance conditions by position pairs.

Related tags

PermutationsLinear ArrangementGap ConditionClass 11Permutations And CombinationsMathematicsClass 11 Mcq
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  5. 5Three distinct prizes are to be awarded to seven students. No student can receive more than one prize. How many ways are possible?
  6. 6If \(\frac{(n+5)!}{(n+3)!}=210\), what is the value of \(n\)?
  7. 7What is the value of \(\frac{21!}{19!\cdot2!}-\frac{18!}{16!\cdot2!}\)?
  8. 8If \(\frac{(n+1)!}{(n-1)!}-\frac{n!}{(n-2)!}=24\), what is the value of \(n\)?
  9. 9What is the value of \(\frac{22!}{20!\cdot 2!}-\frac{21!}{20!}\)?
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