Question

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelops, the probability that all the letters may be placed in wrongly addressed envelopes is.

Answer 1

Answer:

I think I have found a new and simple formula to suit this particular case.

If there is one letter and one envelope then no way you can put it wrong(S1).

If there are 2 letters and 2 envelopes then you can put them wrong in 1 way(S2).

If there are 3 letters and 3 envelopes then you can put them wrong in 2 ways(S3).

If there are 4 then you can put them wrong in 9 ways(S4).

If there are 5 then you can put them wrong in 44 ways(S5).

If you observe you can find a pattern.

S3=(S1+S2)*2

S4=(S2+S3)*3

S5=(S3+S4)*4

S6=(S4+S5)*5

In general, Sn=(Sn-2 + Sn-1)*(n-1)

So, if there are 5 letters then S5=(S3+S4)*4=(2+9)*4=44