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in how many ways 4 letters be selected to form words from the letters BANANA?

sugam Pratap
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  • Did you try to use DictionaryLookup? Although it seems the dictionary does not know about naan, for example – მამუკა ჯიბლაძე Mar 18 '21 at 05:48
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    Are you looking for Permutations[Characters["banana"], {4}]? There are 38 such permutations. –  Mar 18 '21 at 15:09
  • This is unclear what sort of objects you are explicitly trying to count. Do you treat $BANA$ as one of the objects you are counting? Do you treat this the same or different than $NAAB$? They both have the same collection of letters, just in a different order. – JMoravitz Mar 18 '21 at 17:08
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    Assuming order doesn't matter, you can organize your thoughts by listing the outcomes in dictionary order: AAAB, AAAN, AABN, AANN, ABNN, there are only the five outcomes. If order does matter, for each of these listed prior you can count the number of arrangements of them, giving $4+4+12+6+12=38$ – JMoravitz Mar 18 '21 at 17:11
  • I adapted JMoravitz's suggestion here to give a worked example for the more general case of 6-letter combinations from MISSISSIPPI, which for your 4-from-BANANA case would take repetition options of (xxxy,xxyy,xxyz), filled in $(2,1,2)$ ways and permuted in $(4,6,12)$ ways for the same answer. – Joffan Mar 18 '21 at 20:37
  • @JMoravitz yeah you are right here correct answer is 5 here order doesn't matter thank you :) – sugam Pratap Mar 20 '21 at 05:46

1 Answers1

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Assuming order doesn't matter, you can organize your thoughts by listing the outcomes in dictionary order: AAAB, AAAN, AABN, AANN, ABNN, there are only the five outcomes. If order does matter, for each of these listed prior you can count the number of arrangements of them, giving 4+4+12+6+12=38

-@JMmoravitz

sugam Pratap
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