They're 40 students in Joan class she plans to invite them to her birthday party she asked them to suggest a theme for her birthday three of every eight students suggest a rainbow themed party how many students suggested a rainbow theme party how many did not

To find out how many students suggested a rainbow-themed party, we can calculate three-eighths of the total number of students in Joan's class.

1. Total number of students = 40
2. Students suggesting a rainbow theme = \(\frac{3}{8} \times 40\)

Calculating that:

\[
\frac{3}{8} \times 40 = \frac{120}{8} = 15
\]

So, 15 students suggested a rainbow theme party.

Next, to find out how many students did not suggest a rainbow theme party:

3. Students who did not suggest a rainbow theme = Total students - Students who suggested rainbow theme

\[
40 - 15 = 25
\]

Thus, 15 students suggested a rainbow theme party, and 25 students did not.