Well I don't know what i was thinking last time when I wrote this stuff above....[78]
What's only going to change due to the fact that it's multiple-option-correct is the probability that he gets the answer correct, given he guesses it....
Rest can be done as usual considering it to be single option correct, and then the std way of using Baye's theorem.....
Use the classical definition for getting the prob that he correctly guesses the ans viz....
Number of cases possible for the answer to be correct is only 1, since the right combination has to be unique....
Lets now see how many casses are possible for this ......
The boy does not know how many options are correct......
So the reqd no. of possible cases are :-
1) He selects 1 option...
2) He selects 2.....like this,
Thus reqd prob=14C1+4C2+...4C4=115
I hope after this organic can complete it.....if u need the full soln, nudge me!