SOLUTION: A certain machine has nine switches mounted in a row. Each switch has three positions, a, b, and c. A) How many different settings are possible? B) Answer (a) if each position is

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Question 1203686: A certain machine has nine switches mounted in a row. Each switch has three positions, a, b, and c.
A) How many different settings are possible?
B) Answer (a) if each position is used three times.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)   For this machine,  there are   3%5E9 = 19683   different possible settings,  in all.

(b)   I do not understand the meaning of this description and the meaning of this assignment.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The presentation of part B is awkward at best; it appears to be asking the number of possible arrangements of the switch settings there are if there are three each in positions a, b, and c.

The answer is then the number of distinct arrangements of the letters aaabbbccc; by a well-known counting principle, that number of arrangements is

%289%21%29%2F%28%283%21%29%283%21%29%283%21%29%29=362880%2F216=1680

ANSWER: 1680