Answer
The students can be chosen in 19, 448 ways
Step-by-step explanation:
[tex]\begin{gathered} \text{Selection means combination} \\ \text{Total number of students = 17} \\ ^nC_r\text{ = }\frac{n!}{(n\text{ - r)!r!}} \\ n\text{ = 17, and r = 7} \\ ^{17}C_7\text{ = }\frac{17!}{(17\text{ - 7)!7!}} \\ ^{17}C_7\text{ = }\frac{17!}{10!7!} \\ ^{17}C_7\text{ = }\frac{17\text{ x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1}}{10\text{ x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1! 7 x 6 x 5 x 4 x 3 x 2 x 1}} \\ \\ ^{17}C_7\text{ = }\frac{17\text{ x 16 x 15 x 14 x 13 x 12 x 11}}{7\text{ x 6 x 4 x 3 x 2 x 1}} \\ ^{17}C_{7^{}}\text{ = }\frac{98017920}{5040} \\ ^{17}C_7\text{ = 19, 448 ways} \end{gathered}[/tex]