Answer:
a) 2048
b)164
c)54
d) 11
Step-by-step explanation:
a) A coin has two faces.
Outcome possible =2^11= 2048
b) 8 heads possible outcome = 11!/8!3! = 3971688/241/920= 164 ways
c)2 heads outcome= 11!/2!8!= 39716800/725760=54
d) 7 heads= 11!/7!6! =39716800/3628800 = 11
Answer:
2048, 165, 2036, 1816,
Step-by-step explanation:
1. total number of different outcomes for 11 times toss=
[tex]2^{11} = 2048[/tex]
2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn
[tex]11C8 = \frac{11!}{8!(11-8)!}[/tex] = 165
3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes
= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads
= [tex]2^{11} - 11C0 - 11C1[/tex]
= 2036
4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with 8, 9, 10, 11 heads from total number of outcomes
= total number of outcomes - outcomes with 8 heads - outcomes with 9 heads - outcomes with 10 heads -outcomes with 11 heads
=[tex]2^{11} - 11C8 - 11C9 - 11C10 - 11C11[/tex]
=1816
