1. A vehicle license plate number consists of a 3-letter alphabetic block and
a 4-digit numeric block as in XYZ-0516(Note that zero can be a leading digit)
How many license plates
1.1 are there in all?
1.2 show no repetition whatsoever?
1.3 show some repetition in the numeric block? e.g. 0121, 2202, etc.
1.4 use at least one vowel in the alpha block? e.g. BAQ, BEE, etc.
1.5 use "X" or "Y" or both? e.g. ABX, AAY, XXY, etc.
1.6 have 3 distinct letters in alphabetical order? e.g. BQX, CHJ, etc.
2. A phone number is a 7-digit number which is not allowed to start with a zero.
Out of the possible 9 million phone numbers, how many
2.1 do not repeat a digit?
2.2 use exactly 4 zeros? e.g. 320-1000, 200-0220, etc.
2.3 use the 3-digit block "123"? e.g. 412-3666, 512-3123, etc.
2.4 may repeat some digits in the first block of 3 digits but the last four
digits are in strictly increasing order? e.g. 100-1357, 522-0247, etc.
2.5 use exactly 2 digits? e.g. 414-4411, 919-1999, etc.
3. A tour group of 7 persons hand in their passports to their tour leader.
In how many ways can the 7 passports be handed back to the 7 people (one
pass- port to a person) so that
3.1 at least one person gets a wrong passport?
3.2 exactly 2 persons get their own passports?
3.3. nobody gets his own passport?
4. Four people entered a room with 10 chairs to sit. In how many ways can these
four people sit
4.1 where not a single one of them is sitting besides each other?
4.2 where no 2 individuals sit besides each other?
Thank you for any help.
Efren de Luna
Philippines
deluna@misa.irf.ph.net
http://misa.irf.ph.net/~deluna/deluna.html