How many different signals can be sent using at least two?

[Guest]

Five different signal flags are availble to fly on a ship's flagpole. How many different signals can be sent using at least two flags?

I know that for these AT least questions, you got to find the total take away the amount that does not have at least 2 flags in the combination. But Would that total be 2^n= 2^5? cuz then thats only 32..and the answers 320 , how do u do this?

 

[pka]

Do you understand permutations?
\(\displaystyle _n P_k = \frac{{n!}}{{\left( {n - k} \right)!}}\;,\;_5 P_2 = \frac{{5!}}{{3!}} = \left( 5 \right)\left( 4 \right)\)

Then \(\displaystyle \sum\limits_{k = 2}^5 {_5 P_k } = 320.\)

There 320 signals possible, using 2, 3, 4, or 5 flags and permutating them.

 

[soroban]

Re: How many different signals can be sent using at least tw

Hello, Anna!

Five different signal flags are availble to fly on a ship's flagpole.
How many different signals can be sent using at least two flags?

Here is pka's solution . . . in baby steps.

There are: \(\displaystyle \;\left\{\begin{array}{cccc}5\cdot4\cdot3\cdot2\cdot1 &= &120 & \text{ five-flag signals} \\
5\cdot4\cdot3\cdot2 & = & 120 & \text{ four-flag signals} \\
5\cdot4\cdot3 & = & 60 & \text{ three-flag signals} \\
5\cdot4 & = & 20 & \text{two-flag signals} \end{array}\)

Therefore, there are: \(\displaystyle \,120\,+\,120\,+\,60\,+\,20\;=\;320\) signals with at least two flags.