<p>So, I found this question online, but I couldn't find the answer.</p>
<p>There are 30 students in your class. Your science teacher will choose 5 students at random to complete a group project. Find the probability that you and your 2 best friends in the science class are chosen to work in the group.</p>
<p>Is the answer: (28C3*2C2)/30C5 = 2/87 ?</p>
<p>Almost - you have the right idea.</p>
<p>You got the total right: 30C5</p>
<p>The number of successes is 27C2 (3 of the students are fixed - you and your 2 best friends - you now just need to choose 2 more students from the remaining 27).</p>
<p>I hope I got it right myself:
Ok so there are 30 students - the chance of each student to get picked is 1/30. since she is picking 5 students then the probability of the first student is 5/30 (1/6) and the second 4/29 and the third 3/28.multiple those and you get 12/4827 – 1/406.</p>
<p>another way to do this is to sum all the scenarios. this is the combinations available to the teacher:</p>
<p>1/30---- 1/29---- 1/28---- other student ----other student
1/30----- 1/29---- other---- 1/28----- other
1/30 other 1/29 1/28 other
ther will be 5<em>4</em>3<em>2</em>1 of those - 120. but since we don’t care about the order of the others we will only do 5<em>4</em>3 - 60.
1/30 * 1/29 * 1/28 is 1/24360. multiple 60 equals 1/406</p>
<p>hope it helps. if further elaboration is needed i’ll be happy to do so.</p>