How many permutations of the letters a, b, c, d, e, f, g, h have
a...
How many permutations of the letters a, b, c, d, e, f, g, h have
a next to b (in either order: ab or ba) and c not next to d?
How many permutations of the set {A, B, C, D, E, F, G, H}
a) Contain...
How many permutations of the set {A, B, C, D, E, F, G, H}
a) Contain the string DEF?
b) Contain the strings ABE and EFG?
c)Have D next to C?
d) Contain the strings DCB and BAD?
Given that, for some a, b, c, d, e, f, g, h, i ∈ R, [a...
Given that, for some a, b, c, d, e, f, g, h, i ∈ R, [a b c d e f
g h i ] = 5, evaluate the following determinants:
(c) [ka ld mg
kb le mh
kc lf mi] Here, k, l, and m are non-negative constants.
5 -letter "words" are formed using the letters A, B, C, D, E, F,
G. How...
5 -letter "words" are formed using the letters A, B, C, D, E, F,
G. How many such words are possible for each of the following
conditions?
a) No condition is imposed.
b) No letter can be repeated in a word.
c) Each word must begin with the letter A.
d) The letter C must be at the end.
e) The second letter must be a vowel.
in how many ways can six people, a,b,c,d,e and f, be
seated in a row such...
in how many ways can six people, a,b,c,d,e and f, be
seated in a row such that a and b must sit together and c and d
must never sit together?
9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a...
9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a partition of S?
Explain.
b. is {{a, b}, {c, d}, {e, f}, {g, h}, {h, i, j}} a partition
of S? Explain. c. is {{a, b}, {c, d}, {e, f}, {g, h}, {i, j}} a
partition of S? Explain.
Consider lists of length 6 made from the letters A, B, C, D, E,
F, G,...
Consider lists of length 6 made from the letters A, B, C, D, E,
F, G, H. How many such lists are possible if repetition is not
allowed and the list contains two consecutive vowels?
How many integers between 1 and 1000 are divisible by 5? How
many are not divisible by 5?
How many integers between 1 and 9999 have no repeated digits?
How many have at least one repeated digit?