Transcript PreC 09.6 Counting Principle Tic Tac Toe Level 1

9.6 Counting Principle Tic Tac Toe
Press F5. Take turns choosing boxes. The person who chose the box has priority to
answer the problem. If both players get the box wrong, RPS. Please do all 9
problems even if somebody wins.
O
X
O
X
X
O
Box 1
X
O
X
Box 4
X
Box 3
O X
Box 5
O
X
Box 7
X
O
X O
X
O
X O
X
X O
X
O
Box 2
Box 6
O X
Box 8
O X
O
O
Box 9
O
X
O
A customer can choose one of four amplifiers, one of
six compact disc players, and one of eight speaker
models for an entertainment system. Determine the
number of possible system configurations.
4 68
 192 configurations
Box 1
Back to game
A college needs two additional faculty members: a
chemist and a statistician. In how many ways can
these positions be filled if there are three applicants
for the chemistry position and six applicants for the
statistics position?
3 6
 18 ways
Box 2
Back to game
You are taking a chemistry test and are asked to list
the first ten elements in order as they appear in the
periodic table of elements. Suppose you have no
idea of the correct order and simply guess. In how
many different orders could you list the elements?
10  9  8  ...  3  2  1
 10!
Box 3
Back to game
Four people are lining up for a ride on a toboggan,
but only two of the four are willing to take the first
position. With that constraint, in how many ways
can the four people be seated on the toboggan?
2  3  2 1
 12 ways
Box 4
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In a certain state the automobile license plates
consist of two letters followed by a four-digit
number. How many distinct license plate numbers
can be formed?
26  26  10  10  10  10
Box 5
Back to game
In a certain state the automobile license plates
consist of two letters followed by a four-digit
number. To avoid confusion between “O” and “zero”
and “I” and “one,” the letters “O” and “I” are not
used. How many distinct license plate numbers can
be formed?
24  24  10  10  10  10
Box 6
Back to game
How many different ways can 6 children line up in a row?
6  5  4  3  2 1
 6!
Box 7
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You can answer any 8 questions from a total of 14
questions on an exam. In how many different ways
can you select the questions?
14  13  12  11  10  9  8  7
14!

6!
Box 8
Back to game
There are 40 numbers in a particular state lottery.
The first 5 numbers are taken from the same bin
of ping pong balls (no repeating) and the last
number (the Powerball) is taken from its own bin.
How many different ways can a player pick
numbers?
40  39  38  37  36  40
Box 9
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