Chapter 10.5, Problem 34E

To determine

To calculate:

The combinations of two flavors of the vegetable dip are possible

Answer to Problem 34E

The combinations of two flavors of the vegetable dip are $21$ .

  $635376$ .

Explanation of Solution

Given information:

Number of vegetable dip for party: $n=7$

Number of flavors of dip: $r=2$

Calculation:

The formula for permutation for $n$ objects taken $r$ at the time is as:

  $C{}_r=\frac{n!}{\left(n-r\right)!\cdot r!}\cdot \cdot \cdot \left(1\right)$

Where,

  $\begin{array}{l}n=7\\ r=2\end{array}$

Put the values in equation (1)

  $\begin{array}{l}C{}_4=\frac{7!}{\left(7-2\right)!\cdot 2!}\\ C{}_4=\frac{7}{5!\cdot 2!}\\ C{}_4=\frac{7\times 6\times 5!}{5!\times 2\times 1}\\ C{}_4=\frac{7\times 6}{2\times 1}\\ C{}_4=21\end{array}$

Hence, the combinations of two flavors of the vegetable dip are $21$ .