A coin is tossed 11 times. a) How many different outcomes are possible? b) How many different outcomes have exactly 8 heads? c) How many different outcomes have at least 2 heads ? d) How many different outcomes have at most 7 heads?

2048, 165, 2036, 1816,

Step-by-step explanation:

1. total number of different outcomes for 11 times toss=

2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn

= 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

=  

= 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

=

=1816

-4

step-by-step explanation:

do 6-10=

if u need it to be negative.