A hamburger restaurant offers 2 types of buns, 3 types of meat burgers and 4 types of different toppings. How many different hamburgers can be prepared if the chef must choose 1 bun, 1 meat burger but can have no topping, one topping or more than one toppings?
Please verify if my answer is correct:
2C1x3C1x(4C0+4C1)/C9
Thanks in advance
Contrary to probability calculations, we do not need to divide by XC9 when finding the number of arrangements.
C(2,1)*C(3,1) is correct for the first two items.
For the toppings, since we are allowed 0 to 4 toppings, the number of choice available equals the power set, or 2^4.
The total number of arrangements is therefore
C(2,1)*C(3,1)*2^4.
To calculate the number of different hamburgers that can be prepared with the given options, we need to consider the different choices for each component (bun, meat burger, and toppings).
1. Start by selecting one type of bun from the available options. Since there are 2 types of buns, there are 2 choices.
2. Next, choose one type of meat burger from the 3 options. Thus, there are 3 choices.
3. For the toppings, there are three scenarios to consider:
a) No toppings: In this case, you have 0 choices.
b) One topping: You have 4 choices as there are 4 types of toppings to choose from.
c) More than one topping: Since you can choose any combination of the 4 toppings, you can apply the concept of combinations. The total number of combinations for selecting 1, 2, 3, or 4 toppings from a set of 4 is:
- 4C0 + 4C1 + 4C2 + 4C3 + 4C4 = 1 + 4 + 6 + 4 + 1 = 16
4. Finally, multiply the choices for each component together to find the total number of different hamburger combinations:
2 (choices for buns) × 3 (choices for meat burgers) × (0 (no toppings) + 4 (one topping) + 16 (more than one topping)) = 2 × 3 × (0 + 4 + 16) = 2 × 3 × 20 = 120
Therefore, there are 120 different hamburgers that can be prepared with these options.
Regarding your answer, let's break it down:
2C1 represents selecting 1 bun from 2 options, which is correct.
3C1 represents selecting 1 meat burger from 3 options, which is correct as well.
However, (4C0 + 4C1) / C9 is not the correct formulation for selecting the toppings. The denominator (C9) implies selecting 9 toppings which is not in line with the given options. Instead, you should use the correct formulation as explained above.
Hope this clarifies the solution for you!