Answer:
8
Step-by-step explanation:
Total number of students = 17
No. of Freshman = 3
Let the number of sophomore be x
Now we are given that He is going to randomly draw two students to be partners.
He calculates the probability of drawing first a freshman and THEN a sophomore to be [tex]\frac{3}{34}[/tex]
So, probability of drawing a freshman and then a sophomore:
[tex]\frac{^3C_1}{^{17}C_1} \times \frac{^xC_1}{^{16}C_1}=\frac{3}{34}[/tex]
[tex]\frac{3}{17} \times \frac{x}{16}=\frac{3}{34}[/tex]
[tex]x=\frac{3}{34} \times \frac{17}{3} \times 16 [/tex]
[tex]x=8[/tex]
Hence there are 8 Sophomores in the class.
