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I need help to solve this Name: Ch 3 Combinations - 3.1 MDM 4U1 3.1 - Permutations with Non-ordered elements A. Investigation: Permutations with Repeated/Identical

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Name: Ch 3 Combinations - 3.1 MDM 4U1 3.1 - Permutations with Non-ordered elements A. Investigation: Permutations with Repeated/Identical items You are given four blocks: Two white blocks, a red block and a green block. 1. How many ways can you put the items in order, if you treat each of the two white blocks as unique items? (i.e. the white blocks are labeled W, and W2) 2. If the two white blocks are now treated as being identical, how many distinct (i.e. truly different) ways can you put the items in order? Try physically moving the blocks and list all the distinct options to help you. 3. For each of your arrangements of WWRG (where the white blocks are treated as identical), list all the matching/similar arrangements that exist if the white blocks were treated as unique. An example is given. Arrangement of WWRG Matching Arrangements of (White blocks treated as identical) WW2RG (White blocks treated as unique) RGWW RGWW2 or RGWW 4. Notice that, when you have some items that are identical, the number of distinct (i.e. truly different) possibilities is reduced. Can you come up with an expression, using factorials, to show the number of distinct possibilities of 4 items, where 2 of them are identical? 5. Can you come up with a general expression, using factorials, to show the number of distinct possibilities of n items, where a' of them are identical

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