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

magenta Aug 18, 2024

#2**0 **

So what you can do is breaking it up into cases.

Case 1: 10 heads at least

there are a total of 12 flips so you should do 12c10 (combintorics), this is 66

so there are 66 ways for case 1

Case 2: 11 heads at least

12c11 is 12 so 12 ways for case 2

Case 3: 12 heads at least

12c12=1 so there is 1 way for case 3,

If you add them all up you get 79, (66+12+1=79)

Akshara25 Aug 23, 2024