Question 851271
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<pre>

In this problem, the space of events is the set of all possible different groups of 3 persons that can be formed of 7+2 = 9 students.

The number of such groups is  {{{C[9]^3}}} = {{{(9*8*7)/(1*2*3)}}} = 84.

It is the number of events in the space of events.


Of them, the favorable set is the set of all different groups that can be formed of 7 boys.

The number of such groups is  {{{C[7]^3}}} = {{{(7*6*5)/(1*2*3)}}} = 35.


The probability under the problem's question is the ratio of the numer of favorable events (35) to the number of all possible outcomes (84)


    P = {{{35/84}}} = {{{5/12}}} = 0.4167 = 41.67%  (approximately).    <U>ANSWER</U>
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There is another way to get the <U>SAME</U> answer.


<pre>
The probability that the first selected student is a boy is  {{{7/9}}}.

If the first selected student is a boy, then the probability that the second selected student is a boy is  {{{6/8}}}.

If the first and the second selected students are boys, then the probability that the third selected student is a boy is  {{{5/7}}}.

Thus the probability under the problem's question is


    {{{(7/9)*(6/8)*(5/7)}}} = 0.4167 = 41.67%.
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Solved.