Topic
A group of 10 students participated in the Green Summer campaign. The school wants to select a task force with at least two of these students. How many ways are there to set up such a team?
Solution method – See details
Write the general formula and use Newton’s binomial to reduce the expression
Detailed explanation
+ Number of ways to choose 2 students out of 10: \(C_{10}^2\)
+ Number of ways to choose 3 students out of 10: \(C_{10}^3\)
…
+ Number of ways to choose 10 students out of 10 students: \(C_{10}^{10}\)
=> The number of ways to choose is:
\(\begin{array}{l}C_{10}^2 + C_{10}^3 + C_{10}^4 + … + C_{10}^{10} = \left( {C_{10} ^0 + C_{10}^1 + C_{10}^2 + … + C_{10}^{10}} \right) – \left( {C_{10}^0 + C_{10}^1} \right)\\ = {2^{10}} – 1 – 10 = {2^{10}} – 11\end{array}\)
