Answer:
each student gets 3 drinks, make sure the lemon and lime are in different groupings
Step-by-step explanation:
The number of ways to distribute will be 1980.
What is permutation?
The permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
We have,
10 orange drinks
1 lemon drink, and
1 lime drink
And,
Four thirsty students,
Now,
According to the question,
We have to distribute that each student gets at least one drink, and the lemon and lime drinks go to different students.
So,
Using the permutation formula,
Permutation (ⁿPr) = n!/(n-r)!
⁴P₂ = 4! / (4-2)! = (4 × 3 × 2!) / 2! = 4 × 3 = 12
Now,
Using the Combination formula,
Combination (ⁿCr) = n! / [r! (n-r)!]
So,
(ⁿCr) = n! / [r! (n-r)!]
¹¹C₃ = 11! / [ 3!(11-3)!] = [11 × 10 × 9 × 8!] / [ 3 × 2 × 1 × 8!]
¹¹C₃ = 11 × 5 × 3 = 165
So,
The number of ways to distribute = 12 × 165 = 1980
Hence we can say that he number of ways to distribute will be 1980.
To learn more about permutation click here,
https://brainly.com/question/1216161
#SPJ2
