## Solving Lesson 11 Page 39 Math Study Topic 10 – Kite>

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:

$$\begin{array}{l}C_{10}^2 + C_{10}^3 + C_{10}^4 + … + C_{10}^{10} = \left( {C_{10} ^0 + C_{10}^1 + C_{10}^2 + … + C_{10}^{10}} \right) – \left( {C_{10}^0 + C_{10}^1} \right)\\ = {2^{10}} – 1 – 10 = {2^{10}} – 11\end{array}$$