Chapter 10.5, Problem 35E

To determine

To calculate:

The correct value of given expression and analysis the error.

Answer to Problem 35E

The error observed the result of given expression that is $1663200$ .

Explanation of Solution

Given information:

  $\begin{array}{l}{}_{11}{C}_7=\frac{11!}{\left(11-7\right)!}\\ {}_{11}{C}_7=\frac{11!}{4!}\\ {}_{11}{C}_7=9,979,200\end{array}$

Formula used:

Expression for combination

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

Where,

  $n=$ Objects

  $r=$ Time

Calculation:

The denominator of the given expression does not take into account $4!$ . Therefore, the correct number of combinations is as follows:

  $\begin{array}{l}{}_{11}{C}_7=\frac{11!}{\left(11-7\right)!}\\ {}_{11}{C}_7=\frac{11!}{4!}\\ {}_{11}{C}_7=\frac{11\times 10\times 9\times 8\times 7\times 5\times 4!}{4!}\\ {}_{11}{C}_7=1663200\end{array}$

Thus, the value of ${}_{11}{C}_7$ is $1663200$ .

Hence, the error observed the result of given expression that is $1663200$ .