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'n' balls of different colours are placed in 'n' boxes, whose colours are the same as that of the balls. If Pn is the probability that no ball goes into the box its own colour, then
  • a)
    1
  • b)
    e
  • c)
    e-2
  • d)
    e-1
Correct answer is option 'A,B,C'. Can you explain this answer?
Most Upvoted Answer
'n' balls of different colours are placed in 'n' boxes, whose colours...
A permutation in which none of the objects appears in their natural (i.e. ordered) place is called a derangement.
The function giving the number of distinct derangements of n elements is called the sub-factorial !n and is equal to
Here, balls are to be arranged so that no ball goes into the box of its own colour.
Hence, we have to find derangement for n balls.
Number of derangement for n balls
=
Total number of ways that n balls can be arranged among themselves = n!
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'n' balls of different colours are placed in 'n' boxes, whose colours are the same as that of the balls. If Pn is the probability that no ball goes into the box its own colour, then a)1b)ec)e-2d)e-1Correct answer is option 'A,B,C'. Can you explain this answer?
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