Question

There are 17 students in a class, and 7 of them will be chosen to go on a field trip. How many ways can these students be chosen?

Answer 1

The students can be chosen in 19, 448 ways

Explanation:

`\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{ = }(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{ = }(98017920)/(5040) \\ ^(17)C_7\text{ = 19, 448 ways} \end{gathered}`