SOLUTION: 7. How many signals can be made with 5 different flags by raising them any number at a time? Show full solution, thank you!

Question 1191221: 7. How many signals can be made with 5 different flags by raising them any number at a time?
Show full solution, thank you!
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

The flags could either be raised or lowered. We have two options per flag, and 5 flags total.

This gives 2^5 = 32 different configurations.

You can think of it like a binary number of 0s and 1s. Zero could mean "lowered" and 1 could mean "raised".
Or you can think of it like a set of light switches you can flick on or off.

Answer:32

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
How many signals can be made with 5 different flags by raising them any number at a time?
Show full solution, thank you!
~~~~~~~~~~~~~~~~

            As worded, this problem admits different readings, interpretations, solutions and answers.

            See my interpretation, different from that of the other tutor.

            I will assume that 5 flags are NOT ONLY DIFFERENT (they always are different), but distinguished.
            More concretely and for clarity, I will assume that the flags have different colors.

By raising one flag at a time, I can make 5 different signals. By raising two flags at a time, I can make 5*4 = 20 different signals (if to read them from top to bottom, or from left to right). By raising three flags at a time, I can make 5*4*3 = 60 different signals (if to read them from top to bottom, or from left to right). By raising four flags at a time, I can make 5*4*3*2 = 120 different signals (if to read them from top to bottom, or from left to right). By raising five flags at a time, I can make 5*4*3*2*1 = 120 different signals (if to read them from top to bottom, or from left to right). In all, I can make 5 + 20 + 60 + 120 + 120 = 325 different signals, by raising different number of distinguishable flags at a time.

Solved (differently).

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