There should not be a "disconnect between your work and the answer lists exercise 8.6 how many 3-element lists can be formed whose entries are drawn from a pool of n elements - if the first and last entries of the list must be the same? ans. n? a) b) if the first and last entries of the list must be different?

(a) The no. of 3 elements list is

(b) The no. of 3 elements list is

Step-by-step explanation:

As per the question:

Total no. of possible elements = n

The no. of elements required out of n elements to form the list = 3

Now,

(a) When the first and last entries on the list are same:

No. of ways for the entry of first element = n ways

No. of ways for the entry of second element when it can be entered without any restriction = n ways

No. of ways for the entry of last element as it has to be the same as the first element = 1 way  

Thus the total no. of 3 elements list according to the multiplication principle:

(b) When the first and the last entries must be distinct:

No. of ways for the entry of first element = n ways

No. of ways for the entry of second element when it can be entered without any restriction = n ways

No. of ways for the entry of last element as it has to be different from the first element = (n - 1) ways

Thus the total no. of 3 elements list according to the multiplication principle:

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: