Standard Combinatorics

Problem 1) We have 20 kinds of presents; and we have a large supply of each kind. We want to give presents to 12 children. It is not required that every child gets something; but no child can get 2 copies of the same present. In how many ways can we give presents? Problem 2) List all subsets of {a,b,c,d,e} containi ...continues

Complex fraction

[53 / (4-3)/4] - 12 + 1

5(3/3-4/4) -12 +1

5(3/3-4/4) -12 +1

Simplifying Expressions

5 ( 3/3 -4/4) -12 +1

(1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? ...and 4 other questions.

1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?) 2) Find the counterexample to show that the following statemnet is incorrect. "the sum of any odd numbers is divisible by 4. ( I tried several odd numbers and the answer is always divisible by 4) ...continues

Truth tables and De Morgan's Laws

1) Construct a truth table and determine the truth value of the statement ~ q = { ~r ^ ( p v q) }, when p is false, q is true and r is true. 2) Use De Morgan's Laws to determine whether the two statements are equivalent. ~( p ^ q), ~(q v ~p) 3) Determine which, if any of the three statements are equivalent. ...continues

Logic and validity of arguments

Hi Shrikant, I wonder if your can help me with this: 1) Determine whether the argument is valid or invalid. A tree as green leaves or the tree does not produce oxygen. This tree has green leaves. ------------------------------------------------------------- Therefore:. This tree does not produce oxyge ...continues

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the project they have visited. Hannah learned that no two of the other eleven students had shaken the same number of hands. How many hands did Hannah's partner shake?

In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants. No students shook hands with their own partners. After the fair, the students discussed the proje ...continues

Combinatorial Analysis

I have attached chapter 1 description pages. I need following problems. Page 16 : - Problem Number: - 10 Page 17: - Problem Number: - 15 Page 19: - Problem Numbers :- 5 and 8 Please mention each and every step. Thanking you

An automobile manufacturer produces 7 models, each available in 6 different exterior colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of automobiles are available?

An automobile manufacturer produces 7 models, each available in 6 different exterior colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of automobiles are available?