Mathematics, 20.03.2020 09:52 MileenaKitana

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?

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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:

link

Answer from: mcguirefam7071p2mbzz

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 from: Quest

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

Answer from: Quest

step-by-step explanation:

a triangle's full angle is 180 degrees so 180 - 156 = 24. 24/2=12

Plz asap! ! i will award find the value of x in each case. give reasons to justify your solution

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