a) Homes come in 3 designs and 5 heating systems, as well as the choice of a garage or carport. How many choices does that give?
Is this simply the multiplication rule?
b) How many distinct permutations can be made from the letters of the word 'Mississippi'?
If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects taken r at a time, determine the value of r. Is there enough information to determine the value of n? Why or why not?
In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks.
One end of the casing is designated as the top and the other end the bottom.
a) how many different designs are possible
b) If the seven compon
Decide if the situation involves permutations, combination's or neither.
The number of ways 17 people can line up in a row for concert tickets.
Does the situation involve permutations, combination's or neither?
(choose correct answer a, b or c)
a) Permutations. The order of 17 people in line matters.
Consider a non-empty set A. Prove that S(A) is closed in (M(A),o).
Meaning: "o" is the composition of functions which defines a binary operation on M(A), the set of all maps from A to A. You need to prove that the set of all permutations on A is closed under the composition.
For each of the following, express your results in two ways: 1st, using the nPr or nCr notation, whichever is appropriate; 2nd, giving the numerical value:
a) The number of permutations of 8 objects taken 3 at a time
b) The number of combinations of 7 objects taken 5 at a time