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?
1) How many permutations of the letters a, b, c, d, e do not
contain the...
1) How many permutations of the letters a, b, c, d, e do not
contain the string bde.
2) Of any five points chosen within an equilateral triangle
whose sides have length 1, show that at least two of them are
within a distance of 1/2 of each other.
Find the number of permutations of a, b, c, d, e, f, g and h
containing...
Find the number of permutations of a, b, c, d, e, f, g and h
containing no piece ab, or cd, or acb.
Let letters A,B,C,D,E,F,G be used to form strings of length 4.
How many strings of length...
Let letters A,B,C,D,E,F,G be used to form strings of length 4.
How many strings of length 4 with repetitions contain A and B. How
about without repetitions?
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?
We have 1,2,3,4,5,6,7,8,a,b,c,d,e,f
the numbers and letters are in order. How many permutations
(arrangements) are there...
We have 1,2,3,4,5,6,7,8,a,b,c,d,e,f
the numbers and letters are in order. How many permutations
(arrangements) are there in a way that the order is maintained for
numbers and the order is maintained for letters? Explain.
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.
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...
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.