Chapter 8, Problem 90RE

To determine

To calculate: To find the binomial coefficient

Answer to Problem 90RE

  $C{}_{48}=1225$

Explanation of Solution

Given information: $C{}_{48}$

Formula Used:

Identity are

  $C{}_r=C{}_{n-r}$

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

Given the binomial coefficient as $C{}_6$

On solving:

  $\begin{array}{l}C{}_{48}=\frac{50!}{48!\left(50-48\right)!}\\ C{}_{48}=\frac{50!}{48!2!}\\ C{}_{48}=\frac{50\times 49\times 48!}{48!2!}\\ C{}_{48}=\frac{50\times 49}{2!}\\ C{}_{48}=\frac{50\times 49}{2\times 1}\\ C{}_{48}=1225\end{array}$

Conclusion:

Hence, $C{}_{48}=1225$