Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff, if five different flags are available.
Updated On: Jul 6, 2022
$312$
$313$
$315$
$320$
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The Correct Option isD
Solution and Explanation
A signal can consist of either $2$ flags, $3$ flags, $4$ flags or $5$ flags. There will be as many $2$ flag signals as there are ways of filling in $2$ vacant places $\boxminus$ in succession by the $5$ flags available. By Multiplication rule, the number of ways is $5 \times 4 = 20$.
in succession by Similarly, there will be as many $3$ flag signals as there are ways of filling in $3$ vacant places
in succession by the $5$ flags. The number of ways is $5 \times 4 \times 3 = 60$. Continuing the same way, we find that The number of $4$ flag signals $= 5 \times 4 \times 3 \times 2 = 120$ and the number of $5$ flag signals $ = 5 \times 4 \times 3 \times 2 \times 1= 120$ Therefore, the required number of signals $= 20 + 60 + 120 + 120 = 320$.
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
Combination refers to the combination of about n things taken k at a time without any repetition.
The combination is used for a group of data where the order of data does not matter.
