A coin is tossed 13 times a How many different outcomes are

A coin is tossed 13 times. a) How many different outcomes are possible? b) How many different outcomes have exactly 5 heads? c) How many different outcomes have at least 2 heads? d) How many different outcomes have at most 9 heads? You have attempted this problem 0 times. You have 5 attempts remaining.

Solution

n = 13

a ) 2ⁿ = 2¹³ = 8192

b ) Exactly 5 heads = (13!)/(5!.8!) = 1287

c ) At least 2 heads = 8192 - [ (13!)/(0!.13!) + (13!)/(1!.12!) ]

= 8192 - [ 1 + 13 ]

At least 2 heads = 8192 - 14

  At least 2 heads = 8178