Question 1197366
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You should understand the solution shown by tutor @ikleyn.<br>
However, for this particular type of probability problem, there is a much simpler path to the answer.<br>
4 of the 8 people are to be on the committee; the probability that James (or any particular one of them) is on the committee is 4/8 = 1/2.<br>
You can see how this result is obtained by looking at the details of the calculation shown by the other tutor:<br>
{{{C(7,3)/C(8,4)}}}<br>
{{{((7*6*5)/(3*2*1))/((8*7*6*5)/(4*3*2*1))}}}<br>
{{{((7*6*5)/(3*2*1))*((4*3*2*1)/(8*7*6*5))}}}<br>
{{{((7*6*5)/(8*7*6*5))((4*3*2*1)/(3*2*1))}}}<br>
{{{(1/8)(4/1) = 4/8 = 1/2}}}<br>