![]() This, however, assumes all of the letters are unique. How many unique ways are there to arrange the letters in the word CANNON? There are 6 letters in the word CANNON so there are 6! ways to arrange the letters which is 720. A true "combination lock" would accept both 5-10-17 and 17-5-10 as correct. Why is a "combination lock" wrongly named? It should be called a PERMUTATION lock because the order you put in the numbers matters. Order matters in a playlist so we should use permutation.ĪNSWER: There are 2.03 * 10^16 different playlists. How many different 20-song playlists can you make? (order matters) There are 20 songs to be taken 15 at a time. There are 30 songs in your music library. 6 x 5 x 4 / 3 x 2 = 20 This is equivalent to the formula. (6 possible objects in 1st slot x 5 possible objects in 2nd slot x 4 possible objects in 3rd slot ) / ( 3! aka the number of duplicates for each ordering) which is 20. For this reason, the combination formula is the permutation formula divided by the factorial of the number of slots k - because the factorial of k is the number of ways k things can be ordered, aka the number of duplicates for each ordering. In fact, we would count all orderings of the 3 objects A B C (3 FACTORIAL orderings) as one combination. This means that (A, B, C) is the same as (C, B, A). For a combination, order does NOT matter. In other words there are 6 total objects and 3 slots to put them in. This means that there are 6 objects to be taken 3 at a time.
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