Question

Determine the number of elements in the sample space for each of the following:
a. Tossing a coin three times
b. The order that the top 5 students will receive their diplomas.
c. Tossing a pair of dice.

Answer 1

2 possibilities for each coin, by the counting principle it is
\[2\times 2\times 2=2^3\]

Answer 2

c) six possibilities for each die, by the counting principle it is \(6\times 6=6^2\)

Answer 3

b) 5 choices for the first place
4 choices for the second
3 for the third
2 for the fourth
1 for fifth
counting principle say multiply these together get
\[5\times 4\times 3\times 2\times 1=5!\]

Answer 4

thnx