How many permutations of the letters ABCDEFGHIJKLM do not
contain the strings “BAD” or “DIG” or “CLAM” consecutively? (Hint:
Inclusion-exclusion and subtraction).
**I KNOW THE ANSWER IS NOT 13! - 11! - 11! - 10! ** - please do
not give that as one.
1. a. How many permutations are there of the letters
{A,B,C,D,E,F}? Of there, how many are even?
b. Express the permutation BAFEDC in P6 in cycle
notation and determine whether it is even or odd.
c. Determine the composition BAFEDC*BCAFDE in P6. Is
the composition even or odd?
d. What is the members of P6 whose cycle notation
(1345)(26)?
*PERMUTATIONS*
How many tablets of 3 letters and 3 numbers can we form with the
letters {A, B, C, D, E} and the 10 digits if the tablet should
have:
◦ Letters and numbers should be kept together without
repetition?
◦ Letters and numbers should be kept together with
repetition?
◦ Letters and numbers do not have to be kept together without
repetition?
◦ Letters and numbers do not have to be kept together with
repetition?
A seqstring
is a sequence of 18 letters(one of the 26 lowercase letters a-z).
How many seq strings are there where the number of letters between
any two occurences of the same letter is at least
2?
consider “COLLEGEOFENGINEERING”
a) How many permutations are there total?
b) How many permutations start and end with vowels?
c) How many permutations do NOT have consecutive vowels in
them?
d) How many permutations contain the vowels in order (all Es
before All Is before all Os)?
e) How many permutations contain the substring "GINGER"?
Discrete Math: 7) How many 4-element DNA sequences..
a) Do not contain the base T?
b) Contain the sequence ACG?
c) Contain all four bases A, T, C, and G?
d) Contain exactly three of the four bases?
How many ±1-sequences of length n are there?For example, (1, −1,
−1, 1) is not a happy sequence, because although 1 ≥ 0 and 1 − 1 ≥
0,the sum 1−1−1 is negative, so the condition fails for k = 3.