Question 1170786
.
11 out of 15 students is selected for a football team. What is the probability that Hanif is selected?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The total number of all possible teams is the number of combinations

    {{{C[15]^11}}} = {{{(15*14*13*12)/(1*2*3*4)}}} = 1365.


The teams where Hanif participates, are those where 10 other students 
of remaining 15-1 = 14 students participate.


The number of such teams is  {{{C[14]^10}}} = {{{(14*13*12*11)/(1*2*3*4)}}} = 1001.


The probability that Hanif will be selected is  P = {{{1001/1365}}} = 0.7333  (rounded).    <U>ANSWER</U>
</pre>

Solved.



Another reasoning is possible, also.


The probability that Hanif will be among &nbsp;11 &nbsp;lucky guys from the total &nbsp;15 &nbsp;guys is &nbsp;{{{11/15}}}.


Notice that this ratio's value is precisely the same as  &nbsp;{{{1001/1365}}}  &nbsp;above.