Respuesta :
Answer:
Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made = 529,200
Step-by-step explanation:
Given -
A fast-food restaurant offers 6 different burgers, 6 different side orders, 7 different flavor drinks, and 9 different flavors of ice cream .
choose 2 burgers from 6 different burger = [tex]\binom{6}{2}[/tex]
choose 3 different sides from 6 different side orders = [tex]\binom{6}{3}[/tex]
choose 2 flavor drinks from 7 different flavor drinks = [tex]\binom{7}{2}[/tex]
choose 3 ice cream from 9 different flavors of ice cream = [tex]\binom{9}{3}[/tex]
Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made=
= [tex]\binom{6}{2}\times\binom{6}{3}\times\binom{7}{2}\times\binom{9}{3}[/tex] ( Using combination )
= [tex]\frac{6!}{(2!)(4!)}\times\frac{6!}{(3!)(3!)}\times\frac{7!}{(2!)(5!)}\times\frac{9!}{(3!)(6!)}[/tex]
= [tex]15\times20\times21\times84[/tex]
= 529,200
