n this problem, we are dealing with two dimensional arrays

(or matrices) that have 20 rows and 20 columns. Further, each entry

in the array is 1, 2, or 3. Assume that the rows as well as columns are

indexed by 1 through 20.

(a) How many such arrays are there in which 1 is absent from the top row

(and there are no other restrictions)? (

hint:

Build row by row.)

(b) How many such arrays are there in which

either

1 is absent from row 1

or

2 is absent from row 2 (and there are no other restrictions)?

(c) How many different such arrays are there in which

exactly one

1 ap-

pears along the main diagonal (i.e. entries with indices [1][1], [2][2],

,

[20][20]) and there are no other restrictions?