Year 11 Maths - Specialist Principles of counting

Pascals triangle

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Questions

Question 1

56547

Evaluate ${}^8{C_4}$, ${}^7{C_3}$ and ${}^7{C_4}$ and verify that

\[{}^8{C_4}={}^7{C_3}+{}^7{C_4}\]

Answer

True

Worked Solution

$$
\begin{aligned}
{ }^{8} C_{4}&=\frac{8 !}{4 ! 4 !}=70, \quad {}^{7}C_{3}=\frac{7 !}{4 ! 3 !}=35,\
^{7} C_{4}=\frac{7 !}{3 ! .4 !}=35
\\
70&=35+35 \\
\therefore \ { }^{8} C_{4}&={ }^{7} C_{3}+{ }^{7} c_{4}
\end{aligned}
$$

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