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There are 6 letters and 6 self addressed envelopes.What is the probability that atleast 1 is placed correctly??

There are 6 letters and 6 self addressed envelopes.What is the probability that atleast 1 is placed correctly??

Grade:11

2 Answers

Amit Jain
askIITians Faculty 32 Points
10 years ago
If we let A be the event that letter A is in the correct envelope, and 
similarly B is event that letter B is in the correct envelope, then

P(A) = 1/5  

P(A and B) = 1/5 x 1/4

Now use the inclusion, exclusion formula to get the probability that A or 
B or C .... or E are correctly placed.

P(A or B or C .... or E) = P(A) + P(B) + P(C) + P(D) + P(E)
                         - P(A and B) - P(B and C) -....
                         + P(A and B and C) + P(B and C and D) + ....
                         - P(A and B and C and D) - P(...) -......
                         + P(A and B and C and D and E)

                         = 5 x (1/5)
                           - 5C2 x (1/5)(1/4)
                           + 5C3 x (1/5)(1/4)(1/3)
                           - 5C4 x (1/5)(1/4)(1/3)(1/2)
                           + (1/5)(1/4)(1/3)(1/2)(1/1)

      5x4    1     5x4x3      1      5x4x3x2      1          1
 1 - ---- x ---- + ------ x ----- - --------- x ------- + --------
      1x2   5x4    1x2x3    5x4x3    1x2x3x4    5x4x3x2   5x4x3x2x1

      = 1 - 1/2! + 1/3! - 1/4! + 1/5!


This is the probability that at least one letter is correctly placed.
Amit Jain
askIITians Faculty 32 Points
10 years ago
Go from line 16 to line 20 directly as the division is not clearly visible.

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