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:

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.