100 coins,each with a Head and a Tail,are tossed randomly onto a table.A microstate is defined as the number of Heads that appear after the toss.What is the value for the number of Heads that has the most number of microstates?
A) 95
B) 75
C) 60
D) 50

Question

Quizplus · Accepted Answer

The number of possible microstates for n coins with k heads is given by the binomial coefficient ${n\choose k}$. The maximum number of microstates occurs when the number of heads is equal to the number of tails, which is 50 in this case. To see this, note that ${100\choose 50}$ is the largest binomial coefficient for this problem.

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