Pupil pair combinations

Without listing all the possibilities, calculate how many different pairs can be made
A) of 12 pupils who want to go down a water slide on a two-seater inflatable in the water park.
B) of 15 pupils who want to ride toy cars in the amusement park.

Final Answer:

n =  66
b =  105

Step-by-step explanation:

$$\begin{gathered} C_2(12)=\left(\genfrac{}{}{0ex}{}{12}{2}\right)=\frac{12!}{2!(12-2)!}=\frac{12\cdot 11}{2\cdot 1}=66 \\ n=\left(\genfrac{}{}{0ex}{}{12}{2}\right)=66 \end{gathered}$$

$$\begin{gathered} C_2(15)=\left(\genfrac{}{}{0ex}{}{15}{2}\right)=\frac{15!}{2!(15-2)!}=\frac{15\cdot 14}{2\cdot 1}=105 \\ b=\left(\genfrac{}{}{0ex}{}{15}{2}\right)=105 \end{gathered}$$

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