Course title : Discrete Mathematics Structure
Course code : CS 203
Instructors : Dr. Yasser Fouad
Sheet # 6 Counting
(1) How many positive two-digit integers are multiples of 3?
(2) Suppose A[1], A[2], A[3], ..., A[n] is a one-dimensional array and n ≥ 50
(a) How many elements are in the array?
(b) How many elements are in the sub-array A[4], A[5], ..., A[39]?
(3) How many integers are there between 1 and 1001 that are multiples of 3?
(4) How many even integers are there between 1 and 1001?
(5) (a) A bit string is a finite sequence of 0's and 1's. How many bit strings have
length 8?
(b) How many bit strings of length 8 begin with three 0's?
(c) How many bit strings of length 8 begin and end with a 1?
(6) Hexadecimal numbers are made using the sixteen digits 0, 1, 2, ..., 9, A, B, C, D,
E, F. They are denoted by the subscript 16.
(a) How many hexadecimal numbers begin with one of the digits 3 through B,
end with one of the digits 5 through F and are 5 digits long?
(b) How many hexadecimal numbers begin with one of the digits 4 through D,
end with one of the digits 2 through E and are 6 digits long?
(7) Suppose that in a certain state, all automobile license plates have four letters
followed by three digits:
(a) How many different license plates are possible?
(b) How many license plates could begin with TGIF?
(c) How many license plates are possible in which all letters and digits are
distinct?
(d) How many license plates could begin with A and end in 0?
(e) How many license plates could begin with AB and have all letters and digits
distinct?
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(8) (a) How many ways can the letters of the word ALGORITHM are arranged in a
row?
(b) How many ways can the letters of the word ALGORITHM are arranged in a
row if A and L must remain together (in order) as unit?
(9) Write all the 2-permutation of {W, X, Y, Z}.
(10) How many arrangements in a row of no more than three letters can be formed
using letters of the word NETWORK (with no repetitions allowed)?
(11) How many five-digit integers (integers from 10,000 through 99,999) are
divisible by 5?
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(12) List all 2-combinations for the set {x1, x2, x3}. Deduce the value of   .
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Good Luck 
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