a) When the expression (A+ a)(B + b)(C + c)(D + d)(E + e) is
multiplied...
a) When the expression (A+ a)(B + b)(C + c)(D + d)(E + e) is
multiplied out, how many terms will have three uppercase
letters?
b) How many ways are there to pick a combination of k things from
{1, 2,...,n} if the elements 1 and 2 cannot both be picked? d) 2
How many ways are there to put eight rooks on a chessboard so that
no one rook can capture another? (This means that no two are in...
a) How many of the integers from 1 to 1000 are divisible by at
least one...
a) How many of the integers from 1 to 1000 are divisible by at
least one of 3, 5, and 7?
b)(When the expression
(A+ a)(B + b)(C + c)(D + d)(E + e)
is multiplied out, how many terms will have three uppercase
letters?
c) How many ways are there to pick a combination of k things
from {1, 2,...,n} if the elements 1 and 2 cannot both be
picked?
d) 2 How many ways are there to put...
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?
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.
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.
Consider mini-alphabet made of just letters {a, b, c, d, e}. How
many “words” (i.e., strings...
Consider mini-alphabet made of just letters {a, b, c, d, e}. How
many “words” (i.e., strings of letters from that alphabet, whether
they correspond to meaningful words or not) are there of length n,
for n≥1 ? Use mathematical induction to prove your answer.
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?
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?
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.