14.11. References 603
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
:::
BOOK
OBOK
KOBO
:::
(d)What kind of mapping is this, young grasshopper?(e)In light of the Division Rule, how many arrangements are there ofBOOK?(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 ofKE 1 E 2 PE 3 Rto an arrangement of
KEEPERby erasing subscripts. List all the different arrangements ofKE 1 E 2 PE 3 R
that are mapped toREPEEKin this way.
(h)What kind of mapping is this?(i)So how many arrangements are there of the letters inKEEPER?
Now you are ready to face the BOOKKEEPER!
(j)How many arrangements ofBO 1 O 2 K 1 K 2 E 1 E 2 PE 3 Rare there?(k)How many arrangements ofBOOK 1 K 2 E 1 E 2 PE 3 Rare there?(l)How many arrangements ofBOOKKE 1 E 2 PE 3 Rare there?(m)How many arrangements ofBOOKKEEPERare there?
Remember well what you have learned: subscripts on, subscripts off.
This is the Tao of Bookkeeper.(n)How many arrangements ofVOODOODOLLare there?(o)How many length 52 sequences of digits contain exactly 17 two’s, 23 fives,
and 12 nines?