Question
The number of different signals that can be made by 5 flags from 8 flags of different colours is :
 6720



Hint:
We are provided with 8 flags of different colours and 5flags. We need to find the total number of signals that can be made by the number of arrangements of 8 flags by taking 5flags at a time. Arranging things is called permutation, thus we can clearly say that the given question is based on the topic “permutation”. Here we have to arrange 8 flags taken 5flags at a time which is equivalent to filling 8flags placed out of 5flags. For that we have the formula of permutation:
The correct answer is: 6720
Detailed solution
We have been told that there are 8flags of different colours by taking 5flags at a time. Thus the total number of flags n=8and flags to be taken at a time r = 5
By applying the permutation formula =
Thus, the number of different signals that can be made by 5 flags from 8 flags of different colours is 6720.
Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation. The number of permutation without any repetition states that arranging n objects taken r at a time is equivalent to filling r places out of n things =n(n−1)(n−2)......(n−r−1) ways =
Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.
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