Four coins,each with a Head and a Tail,are tossed randomly on to a table.The microstate is defined as the "number of Heads showing".The number of Heads can be,0,1,2,3,4.What value for the "number of Heads showing" has the greatest number of microstates?
A) 0
B) 1
C) 2
D) 3
E) 4

Question

Quizplus · Accepted Answer

The number of microstates for each outcome can be calculated using the binomial coefficient (n choose k), where n is the total number of coins (4) and k is the number of heads.
Thus, the number of microstates for each outcome are:
- 0 heads: (4 choose 0) = 1
- 1 head: (4 choose 1) = 4
- 2 heads: (4 choose 2) = 6
- 3 heads: (4 choose 3) = 4
- 4 heads: (4 choose 4) = 1
Therefore, the outcome with the greatest number of microstates is 2 heads (choice C), with 6 possible arrangements.

Four Coins,each with a Head and a Tail,are Tossed Randomly