Doubt in an approach to solve a probability question There are 6 tickets to a theatre, four of which are for seats in the front row.  3 tickets are selected at random.  What is the probability that two of them are for the front row ?
Process:
I tried 2 approaches , but not able to get the desired answer using the second one
Approach 1 :
(4c2 * 2c1)/(6c3) = 0.6
Explanation :- sample space would be 6c3 and 3 tickets in which 2 are for front row can be chosen in 4c2 ways and the seat other than that of front can be chosen in 2c1 ways , there fore (4c2 * 2c1)/(6c3)
Approach 2 :
Choosing first front seat with a probability of 4/6.
Second front seat can be chosen with a probability of 3/5
and the other seat than the front can then be chosen with 2/4 probability
Also this is fixed for the combination of Front seat, Front seat, Other seat, therefore I'll multiply it with 3! so that all arrangements are taken care of
giving us (4/6) * (3/5) * (2/4) * (3!) = 1.2
Where am I going wrong with my second approach ?
 A: If you multiply by 3! you are over-counting. You're basically counting frontseat, frontseat, backseat as different from frontseat, frontseat, backseat (you are permuting the two frontseat picks and counting them as different even though you shouldn't be).
The reason is that when you assign a 4/6 probability to picking a frontseat on your first pick, you are taking care of all ordered ticket outcomes for which the first seat you picked was a frontseat.
What you should really do is calculate the probability that you obtain frontseat, frontseat, backseat + frontseat, backseat, frontseat + backseat, frontseat, frontseat. This is because there are 3 different ways that you could have chosen the two frontseats (this is dictated by the position of the backseat pick).
As you've correctly stated, all these are the same at 1/5. The total is 3/5 or 0.6, which matches the answer the first method produces.
To get better at these counting problems I highly recommend watching the first 4 lectures from this series: https://www.youtube.com/watch?v=j9WZyLZCBzs&list=PLUl4u3cNGP61MdtwGTqZA0MreSaDybji8
