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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 $5?$

 Dec 16, 2023
 #1
avatar+126978 
+1

Number of possible outcomes  =   2^12

Number where 0 heads were tossed =  1

Number where  1 head was tossed   = 12

Number where 2 heads were tossed  = C (12 ,2)  = 66

Number where 3 heads are tossed = C (12,3) = 220

Number where 4 heads are tossed=  C (12, 4)  = 495

 

Number of different sequences where at least 5 heads were tossed = 

 

2^12 - 1  - 12 - 66 - 220 - 495  =   3302

 

 

cool cool cool

 Dec 16, 2023
 #2
avatar+25 
0

You could use pascal's triangle and find out what it is, looking at the first or last 6 numbers in the 13th row, including the ones at the top, add them together, and substract that from 2^12

 Dec 17, 2023

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