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maths question help help?
Sam has to play 4 songs from a list of 7 songs. Of these 7 songs, 4 were written by Beethoven and 3 songs were written by Mozart.
Find the number of ways the 4 songs can be chosen if there are no restriction. Hence, find the number of ways if there must be 2 songs selected from each composer.
Why can't I use permutation but use combination? anyone can explain?
3 Answers
- Anonymous10 years agoFavorite Answer
If no restriction:
7 songs in total, must choose 4. Therefore:
7C4 which is 7!/(4!x3!)
=35 ways
If 2 songs from each composer itd be:
4C2 x 3C2 which is 4!/(2!x2!) x 3!/(2!x1!)
=18 ways
The reason why you don't use permutations here is that permutations deal with the order in which things are chosen or placed where as combinations only deal with what is chosen and not the order.
In permutations choosing: ABC is different from BAC
In combinations they are the same.
Using the first question as an example, choosing 4 songs out of 7. No matter if you choose ABCD or BACD it's always the same 4 songs, therefore order doesn't matter here.
If the question was reworded "How many arrangements could you make out of 4 songs of the 7?" then you should use permutations as ABCD is a different arrangement to BACD
Hope I helped :D
Source(s): Permutations and Combinations - Anonymous10 years ago
If this is from school don't even bother.. Stupid question. Just gotta sit and write numbers 1-6 continually
