Question 1098788
<br>Since we want the probability that all three are mathematicians, we don't need to worry about the order in which they are chosen.<br>
The probability that the first one selected is a mathematician is 5/13.
The probability that the second one selected is a mathematician is 4/12.
The probability that the third one selected is a mathematician is 3/11.
<br>The probability that all three are mathematicians is {{{(5/13)*(4/12)*(3/11) = 5/143 = 0.0350}}} (approximately).<br>
...or you can use the nCr ("n choose r") concept to find the answer.<br>
The total number of ways of choosing 3 of the 13 people is 13C3 = 286; the number of ways of choosing 3 of the 5 mathematicians is 5C3 = 10; so the probability that the 3 people chosen are all mathematicians is {{{10/286 = 5/143}}}.