WasimAkramKhan wrote:
Vyacheslav wrote:
I3igDmsu wrote:
* A teacher has 15 students and 5 are to be chosen to give demonstrations. How many different ways can the teacher choose the demonstrators given the following conditions.
I think that in this example
order doesn't matter. Could somebody prove/reject, pls
Thanks in advance.
yes order has no work... only combination is req..
I3igDmsu has done a great job of giving sample questions where Order Matters
He is right that being aware of certain keywords helps you determine whether Order Matters in a question or not. However, please note that the words 'Pick' and 'Choose' indicate that order DOES NOT matter. So, the list of keywords provided by I3igDmsu needs to be corrected in this regard.
This also probably explains why WasimAkramKhan asked the follow-up question, which had the keyword 'choose'. In this question, order DOES NOT matter. It is therefore a selection (combination) question.
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While the keywords present in the question statement are of help in clearing the doubt about whether Order Matters or not,
nothing beats conceptual understanding of WHY order matters in a particular case and not in another.Let us try to answer this 'WHY' in the question quoted by WasimAkramKhan above.
Let the 15 students in question be named A, B, C . . . O
The question here asks, in how many ways can the teacher
choose the 5 demonstrators?
So, what can the possible groups of demonstrators be?
Some examples are: (ABCDE), (ABCDF) . . . (BCDEO) etc.
Essentially, we are choosing 5 students out of 15 students here and giving them the label of 'demonstrators'. So, this is a SELECTION question. Order doesn't matter here. The answer will be 15C5
This question also illustrates what we said above: The word 'CHOOSE' indicates that the given question involves Selection (Combination) and that Order doesn't matter.Let us now consider a different question:
A teacher has 15 students and 5 are to be chosen to give demonstrations. In how many ways can the demonstrations be made?Do you see the difference between this question and the previous one? ('ways to choose the demonstrators' v/s 'ways to make the demonstrations')
In the second question, we will have two tasks to perform:
1. Select a group of 5 students to demonstrate
2. Within a selected group of students, decide the order in which the students make the demonstrations.
For example, let the chosen group of demonstrators be: A, B, C, D and E
Now, within this group, we will have to make another decision: Who will demonstrate first of all? Who will be the second to demonstrate and so on . . .
Basically, ORDER MATTERS in this case. So, this is a Permutation question and the answer to this question will be: 15P5
The Takeaways from this discussion:
When in doubt about whether the given question is about Permutation or about Combination,
1. Look for certain helpful keywords
2. Try to imagine the scenario given in the question (maybe with the help of an example) and ask yourself: DOES ORDER MATTER here?Hope this helps!
Japinder
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