The student council at a college is made up of four freshmen, five sophomores, six juniors, and seven seniors. a yearbook photographer would like to line up two council members from each class for a picture. how many different pictures are possible if each group of classmates stands together?

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

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

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