Question 1200086
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        In this problem,  the formulation is  NOT  CONSISTENT  with the answers list.



As the post is worded,  printed,  and presented,  its context means that the order of the three heads and two tails 
is arbitrary.  We can not make other assumptions.


If the order is special,  it  MUST  be pointed in the problem explicitly.


Without special pointing,  the meaning of the post is  UNIQUE,  by default:  the order is  {{{highlight(highlight(arbitrary))}}}.


<pre>
If so, then this problem is a typical binomial distribution 
with the number of trials n=5; the number of success k=3 (head);
and the probability of the individual success p = {{{1/2}}}.


Then the probability under the problem question is

    P = P(n=5; k=3; p=0.5) = {{{C[5]^3*(1/2)^3*(1/2)^2}}} = {{{10*(1/2)^5}}} = {{{10/32}}}.    <U>ANSWER</U>  (which is not in the answers list).
</pre>

Again: &nbsp;as written, &nbsp;the problem admits only one interpretation, regarding the order: &nbsp;the order is &nbsp;ARBITRARY.


If you want interpret in different way, &nbsp;then the wording must be changed adequately .



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a standard rule in &nbsp;Math, interpreting texts by default:


By default, &nbsp;we assume the weakest assumption &nbsp;(which in this case is arbitrary ordering).


Everything which is more special than weakest, &nbsp;must be specified explicitly.