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Subjects
Class 11MathematicsPermutations and CombinationsPermutationsHard
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(7) distinct letters are placed in (7) distinct envelopes. If exactly (5) letters are in correct envelopes, how many ways are possible?

Answer and explanation

Correct answer: (21)

Choose the (2) incorrect letters in (\binom{7}{2}) ways, and they derange in only (1) way. The answer is (21).

Related tags

PermutationsDerangementExactly CorrectPermutations And CombinationsMathematicsClass 11 Mcq
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  2. 2An online form has 4 options for class, 3 options for section, and 5 options for subject. In how many ways can one complete selection of a class, a section, and a subject be made?
  3. 3How many (3)-digit numbers can be formed from digits (1,3,5,7,9) without repetition?
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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 \(\frac{22!}{20!\cdot 2!}-\frac{21!}{20!}\)?
  10. 10If (5) different books are arranged in a row, how many ways are possible?
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