Math Homework help? ( product tables and arrangements)?
I have two problems for my mathematical perspectives class that I don't get.
The first one I have to make a product table and answer a,b,and c.
1. If we roll 2 sixsided dice (numbered 1 to 6), we have 36 possibilities. Build a Product Table for the 2 dice and tell:
a) The number of dice rolls where neither number is Even
b) The number of rolls where both numbers are Perfect Squares
c) The number of rolls where one number is exactly twice the other number
The second problem has to do with arrangements.
2. We have to create passwords for a new computer system. We can use any of 5 letters (a, b, c, d, e) in both upper and lower case and any of 4 digits (0, 1, 2, 3).
a) How many 3character passwords can we create?
b) How many 3character passwords can we create if we cannot repeat any character?
c) Oops! The new system is caseinsensitive (it cannot tell upper case and lower case apart)! How many 3character passwords do we now have?
Help with either would be much appreciated!! Thank you!!
1 Answer
 SamwiseLv 71 month ago
I'm not sure what is meant by a "Product Table" in this case:
Is it a table of the product of the two numbers rolled,
or a table of the number pairs produced?
The first would be the normal meaning of "product,"
but the second makes far more sense, given the following questions,
so that's what I'll assume is meant here.
\ .... 1 .... 2 .... 3 .... 4 .... 5 .... 6 ... < first die
1 . 11 . 21 . 31 . 41 . 51 . 61
2 . 12 . 22 . 32 . 42 . 52 . 62
3 . 13 . 23 . 33 . 43 . 53 . 63
4 . 14 . 24 . 34 . 44 . 54 . 64
5 . 15 . 25 . 35 . 45 . 55 . 65
6 . 16 . 26 . 36 . 46 . 56 . 66

second die
a) The number of dice rolls where neither number is Even
Half the numbers rolled are even, and half (three) are not.
Just as the table for six possible numbers has 6*6=36 entries,
the table for three possible numbers (where neither is even)
has 3*3=9 entries, and is a subset of the table shown.
b) The number of rolls where both numbers are Perfect Squares
1 and 4 are the perfect squares, so that would be a 2 by 2 subset
of the table, and 2*2 = 4 entries.
They are, of course, the entries 11, 14, 41, and 44.
c) The number of rolls where one number is exactly twice the other number
They'd have to be 1 and 2 (which occur as 12 and 21),
2 and 4 (which occur as 24 and 42),
and 3 and 6 (which occur as 36 and 63),
for a total of 6 such rolls.
2. We have to create passwords for a new computer system. We can use any of 5 letters (a, b, c, d, e) in both upper and lower case and any of 4 digits (0, 1, 2, 3).
a) How many 3character passwords can we create?
We have five uppercase letters, five lowercase letters, and four digits to use.
So each character in the password can be any of 14 characters,
and there are
14^3 = 2,744 possible passwords.
b) How many 3character passwords can we create if we cannot repeat any character?
We can have any of 14 choices for the first character,
which will leave 13 choices for the second,
which in turn will leave 12 choices for the third.
So that's
14*13*12 = 2,184 possible passwords.
c) Oops! The new system is caseinsensitive (it cannot tell upper case and lower case apart)! How many 3character passwords do we now have?
That takes away 5 possibilities for each character,
so there are
9 * 8 * 7 = 504 if we cannot repeat a character,
or
9^3 = 729 if we are allowed repeated characters.