Greg W. answered • 07/17/15
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You have a collection of 9 songs. How many ways can you listen to 5 or less songs?
1. If order does not matter then you would use the combination formula. It is any 5 or less; therefore, we can have any 5, or any 4, or any 3, or 2, or 1. Using the combination formula we have 9C5 + 9C4 + 9C3 + 9C2 + 9C1 = 126 + 126 + 84 + 36 + 9 = 381 different combinations of listening to 5 or less songs out of the collection of 9 songs.
2. If order matters then the permutation formula would be used: 9P5 + 9P4 + 9P3 + 9P2 + 9P1 = 15,120 + 3,024 + 504 + 72 + 9 = 18,729 different ways( including their order) to listen to 5 or less songs from the collection of 9 songs.
3. The formula for combinations is C( n, r) = ( n !) / ((n--r)!(r!)), and for
permutations it is P( n, r) = ( n !) / ( n--r) ! So, for example, we want to know the number of combinations of any 5 songs out of a collection of 9 songs we would have: C( n, r) = 9! /((9--5)!( 5!)) = 362,880 / 2880 = 126, which is what we got in paragraph one.
4. For the number of combinations of 5 songs out of the collection of 9 songs, and order matters with each combination we have P( n, r) = (n!) / (n--r)! = 9! / 4! = 362,880 / 24 = 15,120, which is what we got in paragraph two.
1. If order does not matter then you would use the combination formula. It is any 5 or less; therefore, we can have any 5, or any 4, or any 3, or 2, or 1. Using the combination formula we have 9C5 + 9C4 + 9C3 + 9C2 + 9C1 = 126 + 126 + 84 + 36 + 9 = 381 different combinations of listening to 5 or less songs out of the collection of 9 songs.
2. If order matters then the permutation formula would be used: 9P5 + 9P4 + 9P3 + 9P2 + 9P1 = 15,120 + 3,024 + 504 + 72 + 9 = 18,729 different ways( including their order) to listen to 5 or less songs from the collection of 9 songs.
3. The formula for combinations is C( n, r) = ( n !) / ((n--r)!(r!)), and for
permutations it is P( n, r) = ( n !) / ( n--r) ! So, for example, we want to know the number of combinations of any 5 songs out of a collection of 9 songs we would have: C( n, r) = 9! /((9--5)!( 5!)) = 362,880 / 2880 = 126, which is what we got in paragraph one.
4. For the number of combinations of 5 songs out of the collection of 9 songs, and order matters with each combination we have P( n, r) = (n!) / (n--r)! = 9! / 4! = 362,880 / 24 = 15,120, which is what we got in paragraph two.
