Hi
AKY13"Detailed calculations"
Person A has 3 options: b,c,d.
Now, I have split and considered these options as 3 separate cases.
Reason: In slot method, we must first address the slot with maximum constraints. And, in each case, this slot is different. Here's how:
Case 1: Person A gets hat b.
In this case, next slot/person to consider should be the one whose hat is already taken i.e. Person B.
Person B has 3 options to choose from: a,c,d: 3C1
Now, irrespective of whatever Person B chooses from above three, Person C and D are each left with one option each.
So, total options in case 1: 1*3*1*1= 3
Case 2: Person A gets hat c.
In this case, next slot/person to consider should be the one whose hat is already taken i.e. Person C.
Person C has 3 options to choose from: a,b,d: 3C1
Now, irrespective of whatever Person C chooses from above three, Person B and D are each left with one option each.
So, total options in case 1: 1*3*1*1= 3
Case 3: Person A gets hat d.
In this case, next slot/person to consider should be the one whose hat is already taken i.e. Person D.
Person D has 3 options to choose from: a,b,c: 3C1
Now, irrespective of whatever Person D chooses from above three, Person B and C are each left with one option each.
So, total options in case 1: 1*3*1*1= 3
Sum of favorable outcomes from above three cases: 9
Total possible outcomes: 4!
Probability: 9/24= 3/8
Ans D
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