Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 649 — #657
15.11. References 649
Exam Problems
Problem 15.25.
Suppose that two identical 52-card decks are mixed together. Write a simple formula
for the number of distinct permutations of the 104 cards.
Problems for Section 15.6
Class Problems
Problem 15.26.
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
O 1 BO 2 K
KO 1 BO 2
BO 1 O 2 K
BO 2 O 1 K
: : :
(d) What kind of mapping is this, young grasshopper?
BOOK
OBOK
KOBO
: : :
(e) In light of the Division Rule, how many arrangements are there of BOOK?
(f) Very good, young master! How many arrangements are there of the letters in
KE 1 E 2 PE 3 R?
(g) 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.