SOLUTION: In a pick 6 lottery game, ten balls labeled zero through nine are placed ina jar and selected one at a time, without replacement. To win, you must match all six in any order. How m

Question 167636: In a pick 6 lottery game, ten balls labeled zero through nine are placed ina jar and selected one at a time, without replacement. To win, you must match all six in any order. How many possible sets of six numbers are there?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since order does not matter (the balls can be arranged in any order), we must use the combination formula:

Start with the combination formula

Plug in and

Subtract to get 4

Expand 10!

Expand 4!

Cancel

Simplify

Expand 6!

Multiply 10*9*8*7*6*5 to get 151,200

Multiply 6*5*4*3*2*1 to get 720

Divide

So 10 choose 6 (where order doesn't matter) yields 210 unique combinations

So there are 210 possible ways to pick 6 numbers from a pool of 10 numbers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a pick 6 lottery game, ten balls labeled zero through nine are placed in a jar and selected one at a time, without replacement. To win, you must match all six in any order. How many possible sets of six numbers are there?
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10C6 = 210
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Cheers,
Stan H.

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