Chapter 6.1, Problem 39E

Solution

To find the number of ways the students can be chosen to represent the senior class on the students council.

The total number of ways in which five students can be chosen in $\text{13836130056}$.

Given information:

Five students to be chosen from 280 students.

Formula used:

  $C{}_r=\frac{n!}{\left(n-r\right)!\cdot r!}$

Calculation:

Five students out of 280 students can be chosen in $C{}_5$.

Evaluate $C{}_5$.

  $\begin{array}{c}C{}_5=\frac{280!}{\left(280-5\right)!\cdot 5!}\\ =\frac{280!}{275!\cdot 5!}\\ =\frac{280\times 279\times 278\times 277\times 276\times 275!}{275!\cdot 5!}\\ =\frac{280\times 279\times 278\times 277\times 276}{5!}\\ =\frac{280\times 279\times 278\times 277\times 276}{120}\\ =\text{13836130056}\end{array}$

Conclusion:

The total number of ways in which five students can be chosen in $\text{13836130056}$.