Hi Sam,
Let's look at some smaller problems.
A fair four-faced die with faces numbered 1,2,3 and 4 is tossed once and the number is recorded. How many numbers are possible?
This is almost too easy. The possible numbers are 1, 2, 3 and 4.
A fair four-faced die with faces numbered 1,2,3 and 4 is tossed twice and the sequence of numbers is recorded. How many sequences are possible?
Each of the possible numbers in the previous problem could be followed by a 1, 2, 3 or 4. Thus the possible sequences are
11 |
12 |
13 |
14 |
21 |
22 |
23 |
24 |
31 |
32 |
33 |
34 |
41 |
42 |
43 |
44 |
Thus there are 4 4 = 42 = 16 possible sequences.
A fair four-faced die with faces numbered 1,2,3 and 4 is tossed three times and the sequence of numbers is recorded. How many sequences are possible?
Each of the possible numbers in the previous problem could be followed by a 1, 2, 3 or 4. Thus there are four times as many three number sequences as there are two number sequences. Thus there are 42 4 = 43 three number sequences. A slightly different way to say this is that there are 4 options for the first number, 4 options for the second number and 4 options for the third number and hence 4 4 4 = 43 possibilities in total.
Now try your problem.
Penny
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