MediumMathematicsHigh School (11–12)Algebra › Permutations and CombinationsNumericalConceptualBoard Exam
A ship has 5 different flags. A signal is made by hoisting at least 2 of them, one above another…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ship has different flags. A signal is made by hoisting at least of them, one above another, on a mast. The order of the flags matters. How many different signals can be made?
Need a reminder? The key ideaShow
A permutation is an arrangement in a definite order. The number of ways to arrange of different objects is , with . If repeats are allowed, there are arrangements.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Split by size. A signal uses , , or flags, and these cases do not overlap.
Step 2. Count each case.
- flags: .
- flags: .
- flags: .
- flags: .
Step 3. Add. .
Answer: signals.
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