A coin is flipped 10 times where each flip comes

danrussekme

danrussekme

Answered question

2021-12-04

A coin is flipped ten times, resulting in either heads or tails on each flip. How many possible outcomes contain at most three tails?

Answer & Explanation

James Kilian

James Kilian

Beginner2021-12-05Added 20 answers

Step 1 
Definitions 
If an event can happen in m ways and a subsequent event can happen in n ways, the product rule applies, then the number of ways that the two events can occur in sequence is then m*n. 
Definition permutation (order is important): 
P(n,r)=n!(nr)! 
Definition combination (order is not important): 
C(n,r)=(nr)=n!r!(nr)! 
with n!=n*(n-1)*...*2*1. 
Step 2 
The order of the heads/tails is not important (since we are interested in the number of heads, not the order of the heads), thus we need to use the definition of combination. 
n=10 
r2 
Consider the following when defining a combination:
C(10,0)=10!0!(100)!=10!0!10!=1 
C(10,1)=10!1!(101)!=10!1!9!=10 
C(10,2)=10!2!(102)!=10!2!8!=45 
C(10,3)=10!3!(103)!=10!3!7!=120 
Add the number of outcomes for each value of r: 
120+45+10+1=176

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