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MIT6_042JF10_rec15

MIT6_042JF10_rec15 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science November 3, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 15 1 The Tao of BOOKKEEPER In this problem, we seek enlightenment through contemplation of the word BOOKKEEPER . 1. In how many ways can you arrange the letters in the word POKE ? 2. 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. 3. 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 . . . 4. What kind of mapping is this, young grasshopper? 5. In light of the Division Rule, how many arrangements are there of BOOK ?
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2 Recitation 15 6. Very good, young master! How many arrangements are there of the letters in KE 1 E 2 PE 3 R ? 7. Suppose we map each arrangement of KE 1 E 2 PE 3 R to an arrangement of KEEPER by erasing subscripts. List all the different arrangements of KE 1 E 2 PE 3 R that are mapped to REPEEK in this way. 8. What kind of mapping is this? 9. So how many arrangements are there of the letters in KEEPER ? 10. Now you are ready to face the BOOKKEEPER! How many arrangements of BO 1 O 2 K 1 K 2 E 1 E 2 PE 3 R are there? 11. How many arrangements of BOOK 1 K 2 E 1 E 2 PE 3 R are there?
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