## Precalculus (6th Edition) Blitzer

a) The value of $nCr$ for $n=8$ and $r=3$ is $\underline{56}$ and is verified. b) The value of $nCr$ for $n=7$ and $r=2$ is $\underline{21}$ and is verified c) The value of $nCr$ for $n=12$ and $r=1$ is $\underline{12}$ and is verified d)The value of $nCr$ for $n=11$ and $r=1$ is $\underline{11}$ and is verified e)The value of $nCr$ for $n=6$ and $r=6$ is $\underline{1}$ and is verified f)The value of $nCr$ for $n=15$ and $r=2$ is $\underline{105}$ and is verified g)The value of $nCr$ for $n=100$ and $r=2$ is $\underline{4,950}$ and is verified h)The value of $nCr$ for $n=100$ and $r=98$ is $\underline{4,950}$ and is verified
(a) Obtain the value of \left( \begin{align} & 8 \\ & 3 \\ \end{align} \right) as follows: \begin{align} & 8\text{ }nCr\text{ 3 } \\ & \text{ 56} \\ \end{align} Thus, the value of \left( \begin{align} & 8 \\ & 3 \\ \end{align} \right)=56 and is the same as one obtained before. (b) The value of \left( \begin{align} & 7 \\ & 2 \\ \end{align} \right) is found as follows: \begin{align} & 7\text{ }nCr\text{ 2} \\ & \text{ 21} \\ \end{align} Thus, the value of \left( \begin{align} & 7 \\ & 2 \\ \end{align} \right)=21 and is the same as one obtained before. (c) The value of \left( \begin{align} & 12 \\ & 1 \\ \end{align} \right) is found as follows: \begin{align} & 12\text{ }nCr\text{ 1} \\ & \text{ 12} \\ \end{align} Thus, the value of \left( \begin{align} & 12 \\ & 1 \\ \end{align} \right)=12 and is the same as one obtained before. (d) The value of \left( \begin{align} & 11 \\ & 1 \\ \end{align} \right) is found as follows: \begin{align} & \text{11 }nCr\text{ 1} \\ & \text{ 11} \\ \end{align} Thus, the value of \left( \begin{align} & 11 \\ & 1 \\ \end{align} \right)=11 and is the same as one obtained before. (e) The value of \left( \begin{align} & 6 \\ & 6 \\ \end{align} \right) is found as follows: \begin{align} & \text{6 }nCr\text{ 6} \\ & \text{ 1} \\ \end{align} Thus, the value of \left( \begin{align} & 6 \\ & 6 \\ \end{align} \right)=1 and is the same as one obtained before. (f) Obtain the value of \left( \begin{align} & 15 \\ & 2 \\ \end{align} \right) as follows: \begin{align} & \text{15 }nCr\text{ 2} \\ & \text{ 105} \\ \end{align} Thus, the value of \left( \begin{align} & 15 \\ & 2 \\ \end{align} \right)=105 and is the same as one obtained before. (g) The value of \left( \begin{align} & 100 \\ & 2 \\ \end{align} \right) is found as follows: \begin{align} & \text{100 }nCr\text{ 2} \\ & \text{ 4950} \\ \end{align} Thus, the value of \left( \begin{align} & 100 \\ & 2 \\ \end{align} \right)=4,950 and is the same as one obtained before. (h) The value of \left( \begin{align} & 100 \\ & 98 \\ \end{align} \right) is found as follows: \begin{align} & \text{100 }nCr\text{ 98} \\ & \text{ 4950} \\ \end{align} Thus, the value of \left( \begin{align} & 100 \\ & 98 \\ \end{align} \right)=4,950 and is the same as one obtained before.