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how many different combinations of 6 numbers from a group of 53 numbers are there assuming you cant repeat a used number

 May 20, 2015

Best Answer 

 #1
avatar+129839 
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We have 53 ways to pick the first number, 52 ways to pick the second, 51 ways to pick the third, etc. =

 

53 x 52 x 51 x 50 x 49 x 48  =  16,529,385,600   combinations

 

But, we need to divide this by   6!  = 720  because the set [21, 33, 2, 5, 19, 6], for example,  has 720 different arrangements

 

So ..  16,529,385,600 . 720  = 22, 957, 480

 

Note that this is exactly the same as  C(53, 6)......!!!

 

 

 May 20, 2015
 #1
avatar+129839 
+5
Best Answer

We have 53 ways to pick the first number, 52 ways to pick the second, 51 ways to pick the third, etc. =

 

53 x 52 x 51 x 50 x 49 x 48  =  16,529,385,600   combinations

 

But, we need to divide this by   6!  = 720  because the set [21, 33, 2, 5, 19, 6], for example,  has 720 different arrangements

 

So ..  16,529,385,600 . 720  = 22, 957, 480

 

Note that this is exactly the same as  C(53, 6)......!!!

 

 

CPhill May 20, 2015

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