Answer:
7257600
Step-by-step explanation:
Number of freshmen in the student council= 4
Number of sophomores in the student council= 5
Number of juniors in the student council= 6
Number of seniors in the student council= 7
Ways of choosing council members
⁴C₂×⁵C₂×⁶C₂×⁷C₂
![^4C_2=\frac{4!}{(4-2)!2!}\\=\frac{24}{4}=6\\\\^5C_2=\frac{5!}{(5-2)!2!}\\=\frac{120}{12}=10\\\\^6C_2=\frac{6!}{(6-2)!2!}\\=\frac{720}{48}=15\\\\^7C_2=\frac{7!}{(7-2)!2!}\\=\frac{5040}{240}=21](https://tex.z-dn.net/?f=%5E4C_2%3D%5Cfrac%7B4%21%7D%7B%284-2%29%212%21%7D%5C%5C%3D%5Cfrac%7B24%7D%7B4%7D%3D6%5C%5C%5C%5C%5E5C_2%3D%5Cfrac%7B5%21%7D%7B%285-2%29%212%21%7D%5C%5C%3D%5Cfrac%7B120%7D%7B12%7D%3D10%5C%5C%5C%5C%5E6C_2%3D%5Cfrac%7B6%21%7D%7B%286-2%29%212%21%7D%5C%5C%3D%5Cfrac%7B720%7D%7B48%7D%3D15%5C%5C%5C%5C%5E7C_2%3D%5Cfrac%7B7%21%7D%7B%287-2%29%212%21%7D%5C%5C%3D%5Cfrac%7B5040%7D%7B240%7D%3D21)
⁴C₂×⁵C₂×⁶C₂×⁷C₂=6×10×15×21=18900
Ways of lining up the four classes=4!=1×2×3×4=24
Ways of lining up members of each class=2⁴=2×2×2×2=16
Pictures are possible if each group of classmates stands together
⁴C₂×⁵C₂×⁶C₂×⁷C₂×4!×2⁴
=18900×24×16
=7257600