MIT6_042JS10_lec28_prob

MIT6_042JS10_lec28_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 14 Prof. Albert R. Meyer revised April 6, 2010, 985 minutes In-Class Problems Week 10, Wed. Problem 1. The Tao of BOOKKEEPER: we seek enlightenment through contemplation of the word BOOKKEEPER . (a) In how many ways can you arrange the letters in the word POKE ? (b) In how many ways can you arrange the letters in the word BO 1 O 2 K ? Observe that we have subscripted the O’s to make them distinct symbols. (c) Suppose we map arrangements of the letters in BO 1 O 2 K to arrangements of the letters in BOOK by erasing the subscripts. Indicate with arrows how the arrangements on the left are mapped to the arrangements on the right. O 2 BO 1 K KO 2 BO 1 BOOK O 1 BO 2 K OBOK KO 1 BO 2 KOBO BO 1 O 2 K ... BO 2 O 1 K ... (d) What kind of mapping is this, young grasshopper? (e) In light of the Division Rule, how many arrangements are there of BOOK ? (f)
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MIT6_042JS10_lec28_prob - Massachusetts Institute of...

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