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kari74 [83]
2 years ago
11

In the california state lottery, you must select six numbers from fifty-two numbers to win the big prize. the numbers do not hav

e to be in a particular order. what is the probability that you will win the big prize if you buy one ticket?
Mathematics
1 answer:
Stolb23 [73]2 years ago
3 0

C(n,r) = [n!/((n-r)!*r!)]  
.  
n is the number of possibilities and it is 52 in question and r is the number of  
things to be taken at a time which is 6  
.  
if we substitiue  
.  
C(n,r) = [52!/((52-6)!*6!)= 52!/((46)!*6!)]  
.  
52! = 52*51*49*48*47*46*45*44*43*42*..... and 46! = 46*45*44*43*42*....  
.
  
you divide 52! by 46! the result after canceling all the   
common terms is just 52*51*50*49*48*47. The question is reduced to    
.  
C(n,r) = (52*51*50*49*48*47)/6!  
.  
and 6! = 6*5*4*3*2*1  
.  
If you want you can divide the numbers from 6! into the numbers in the numerator to simplify  
things a little or you can just take your calculator and multiply out the numerator and  
then divide that answer by 720 which is what 6! equals.  
.  
If you just multiply out the numerator your calculator should tell you that the answer is   
1.46581344*10^10 and when you divide that by 720 you get 20,358,520. This means that for  
every 20,358,520 lottery tickets sold there is likely to be 1 winner among them. Pretty slim  
odds of your ticket being that one.  
.  

If you have a cheap scientific calculator you might examine it carefully to see if it has  
a key function labeled nCr. If you do it will calculate this combination automatically.  
.  
Just enter 52, then press the nCr function, then enter 2, and press the equal sign.
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Step-by-step explanation:

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24    2       24 = 2³ * 3        36    2   36 = 2²*3³         42   2   42 = 2*3*7

12     2                                 18    2                              21   3

6      2                                   9    3                                7   7

3      3                                   3    3                                1

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24 ÷  6      =  4

36 ÷  6      =  6

42 ÷  6      =  7

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