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

Hello..

If 1 letter and 1 envelope then then you can't put wrong (S1).
If 2 letters and 2 envelopes then 1 can be wrong (S2).
If 3 letters and 3 envelopes then 2 can be wrong (S3).
If 4 then you can put wrong in 9 ways(S4).
If 5 then it can put wrong in 44 ways(S5).
Now you can find a pattern.
S3=(S1+S2)*2
S4=(S2+S3)*3
S5=(S3+S4)*4
S6=(S4+S5)*5
= Sn=(Sn-2 + Sn-1)*(n-1)
if 5 letters then S5=(S3+S4)*4=(2+9)*4=44