Virginia Lottery 1992
******Combination Games*******
********MORE ON COMBINATIONS************
******Combination Games*******
Price is Right
"Pick a Pair"
6 items pick the two priced the same.
********MORE ON COMBINATIONS************
Suppose the State Lottery takes this form:
6 numbers are randomly chosen from 1 thru 49.
The customer picks 6 numbers.
If the person matches the 6 that were chosen by the State Committee,
they win the entire JACKPOT.
Sometimes this JACKPOT is over $20,000,000.
If the customer was able to buy EVERY POSSIBLE
COMBINATION of 6 numbers, they would have to win.
How many GROUPS of 6 are possible from
the 49 numbers?
In Math we call this 49 CHOOSE 6
or 49 COMBINATION 6
49 objects GROUPED 6 at a time
Some types of word problems are easily solved using Combinations:
Suppose that you are going to choose a small group of 3 items
from a larger group of 7 items.
You could list all the possible groups, if need be.
But, you can count the number of the possible groups
by just using COMBINATIONS.
7 choose 3 has _35__ possible groups
7! / (3! times 4!) = 35
(7*6*5*4*3*2*1*)
(3*2*1)(4*3*2*1)
Reduce by dividing top
and bottom by (4!)
= (7*6*5)/(3*2*1)
OR
LOOKING at PASCAL's TRIANGLESee the row with 1, 7, 21, 35, 35, 21, 7, 1?
7 choose NONE has _1_ possible group
7 choose 1 has _7_ possible groups
7 choose 2 has _21_ possible groups
7 choose 3 has _35_ possible groups
7 choose 4 has _35_ possible groups
7 choose 5 has _21_ possible groups
7 choose 6 has _7_ possible groups
7 choose 7 has _1_ possible groups
HOW ABOUT using the TI-83?
7 choose NONE has _1_ possible group
7 choose 1 has _7_ possible groups
7 choose 2 has _21_ possible groups
7 choose 3 has _35_ possible groups
7 choose 4 has _35_ possible groups
7 choose 5 has _21_ possible groups
7 choose 6 has _7_ possible groups
7 choose 7 has _1_ possible groups
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This forms Sierpiński triangle
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