Chapter 13.9, Problem 28PPS

To determine

To Find: Number of three toppings hamburgers.

Answer to Problem 28PPS

There are $6$ ways of selecting the toppings and The number of three topping hamburgers is $20$ .

Explanation of Solution

Given information:

Toppings for hamburgers: ketchup, mustard, lettuce, onions and cheese.

Calculation:

The main objective is to find out whether a ordering the hamburger with three toppings represent a combination or permutation and no of three topping hamburgers.

As for selecting the hamburger with three toppings, order is not important.

So, ordering the hamburger with three toppings basically represents a combination.

No of three topping hamburgers is equal to $C\left(6,3\right)$

Now, calculate no. of three topping hamburger is as below:

  $C\left(6,3\right)=\frac{P\left(6,3\right)}{No.ofwaysinwhicheachsetcanbearranged}$

There are $\mathrm{3.2.1}=6$ ways of selecting the toppings.

Calculate $P\left(6,3\right)$ as below:

From $6$ toppings take $3$ at one time and calculate $P\left(6,3\right)=\mathrm{6.5.4}$

Thus,

  $\begin{array}{l}C\left(6,3\right)=\frac{\mathrm{6.5.4}}{\mathrm{3.2.1}}\\ =20\end{array}$

The number of three topping hamburgers is $20$ .