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A coin is tossed $12$ times. How many different sequences of tosses could there have been, if the number of heads was at least $5?$

 Jun 3, 2024
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At least 5 heads means the same as no more than 4 tails

 

0 tails = C(12,0) =  1 possible sequence

 

1 tail  = C(12,1) =    12 possible sequences

 

2 tails =  C(12,,2)  =   66 possible sequences

 

3 tails  = C(12, 3)  = 220 possible sequences

 

4 tails  = C (12,4)  =  495 possible sequences

 

At least 5 heads =   sum of 12rh row of Pascal's Triangle - ( 1 + 12 + 66 + 220 + 495)  =

 

2^12 - ( 1 + 12 + 66 + 220 + 495)  = 

 

3302 possible sequences

 

cool cool cool

 Jun 3, 2024

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