Question

In the school cafeteria, students choose their lunch from 4 sandwiches, 3 soups, 3 salads, and 2 drinks. How many different lunches are possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink?

Answer 1

Answer:

72 different lunches

Step-by-step explanation:

As the student will pick one of each type, we can calculate the number of possibilities for each case, and them multiply all of them.

(if the student picks 1 in a group of 4, the number of different combinations we can do is 4)

For sandwiches, the student has 4 different combinations.

For soups, the student has 3 different combinations.

For salads, the student has 3 different combinations.

For drinks, the student has 2 different combinations.

So, the number of different lunches the stundent can make is 4*3*3*2 = 72

Answer 2

In the school cafeteria, students choose their lunch from 4 sandwiches, 3 soups, 3 salads, and 2 drinks. There are 72 different lunches possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink.

The combination of an object is the technique applied in choosing the possible number of combinations in an array of datasets.

It is can be expressed by using the formula:

$\mathbf{^nC_r =\dfrac{n!}{r!(n-r)!}}$  

where;  

• $\mathbf{^nC_r }$ =  number of combinations
• n = total no. of objects in the data set
• r = no of objects to be chosen in the data set.

To determine the number of different lunches that are possible in which students in the school cafeteria choose exactly 1 sandwich, 1 soup, 1 salad, and 1 drink, we have:

$\mathbf{^nC_r =\dfrac{4!}{1!(4-1)!} \times \dfrac{3!}{1!(3-1)!} \times \dfrac{3!}{1!(3-1)!} \times \dfrac{2!}{1!(2-1)!} }$

$\mathbf{^nC_r =\dfrac{4!}{1!(3)!} \times \dfrac{3!}{1!(2)!} \times \dfrac{3!}{1!(2)!} \times \dfrac{2!}{1!(1)!} }$

$\mathbf{^nC_r =\dfrac{4\times 3!}{1!(3)!} \times \dfrac{3\times 2!}{1!(2)!} \times \dfrac{3\times 2!}{1!(2)!} \times \dfrac{2\times 1!}{1!(1)!} }$

$\mathbf{^nC_r =4\times 3 \times 3 \times 2}$

$\mathbf{^nC_r =72 }$

Therefore, we can conclude that there are 72 different lunches possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink.

Learn more about combinations here:

https://brainly.com/question/8018593?referrer=searchResults