A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes contain exactly two heads?

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Royce Moore · Accepted Answer

Step 1  Definitions  Product rule if one event can occur in m ways AND a second event can occur in n ways, 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!(n−r)!  Definition combination (order is not important):  C(n,r)=(nr)=n!r!(n−r)!  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  r=2  Evaluate the definition of a combination:  C(10,2)=10!2!(10−2)!=10!2!8!=45

A coin is flipped 10 times where each flip comes

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