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

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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) About Me  (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:


n%21%2F%28n-r%29%21r%21 Start with the combination formula



10%21%2F%2810-6%29%216%21 Plug in n=10 and r=6



10%21%2F4%216%21 Subtract 10-6 to get 4


Expand 10!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%216%21


Expand 4!
%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%296%21



%2810%2A9%2A8%2A7%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%296%21 Cancel



%2810%2A9%2A8%2A7%2A6%2A5%29%2F6%21 Simplify


Expand 6!
%2810%2A9%2A8%2A7%2A6%2A5%29%2F%286%2A5%2A4%2A3%2A2%2A1%29



151200%2F%286%2A5%2A4%2A3%2A2%2A1%29 Multiply 10*9*8*7*6*5 to get 151,200



151200%2F720 Multiply 6*5*4*3*2*1 to get 720



210 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) About Me  (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.