Chapter 11.7, Problem 3E

To determine

To calculate: The number of combinations.

Answer to Problem 3E

  ${}_2{C}_1\text{ is equal to 2}\text{.}$

Explanation of Solution

Given information:

Consider the information provided in the question:

  ${}_2{C}_1$

Formula used:

To find the number of combinations of $n$ objects taken $r$ at a time, divide the number of permutations of $n$ objects taken $r$ at a time by $r!$

  ${}_n{C}_r=\frac{{}_n{P}_r}{r!}$

Calculation:

As per the problem,

  ${}_2{C}_1$

To calculate the number of combinations, use formula

  ${}_n{C}_r=\frac{{}_n{P}_r}{r!}$

Substitute $\text{2 for }n\text{ and 1 for }r$

  ${}_2{C}_1=\frac{{}_2{P}_1}{1!}$

  $=\frac{2}{1}$ [Write ${}_2{P}_1$ and $1!$ as products]

  $=2$ [Simplify]

Hence,

  ${}_2{C}_1\text{ is equal to 2}\text{.}$