Answer to Question #281835 in Mechanical Engineering for john luvis

Question

Consider a system of three flipped coins. According to classical statistics,

how many different arrangements are available to this system:

(a) if the coins are distinguishable,

(b) if the coins are identical?

(c) For what fraction of the arrangements in (a) are all three heads or all

three tails?

(d) What is the true number of different heads/tails configurations available

to a system of three identical flipped coins?

(e) For what fraction of these arrangements are all three heads or all three

tails

Answer 1

Assume a capital letter is the head and the small letter is the tail.

(a) The number of arrangements is

ABC, aBC, AbC, ABc, abC, Abc, aBc, abc, or 8 arrangements.

(b) The number of arrangements is

AAA, aAA, aaA, aAa, AaA, aaa, or 6 arrangements.

(c) Distinguishable: 1/8 is all three heads and 1/8 is all three tails.

(d) aAA, aaA, aAa, AaA, or 4.

(e) Distinguishable: 1/8 is all three heads and 1/8 is all three tails. Identical: 1/6 is all three heads, 1/6 is all three tails.