Question

A fast-food restaurant offers 6 different burgers, 6 different side orders, 7 different flavor drinks, and 9 different flavors of ice cream. In how many ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made?

Answer 1

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

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 =
`\binom{6}{2}`

choose 3 different sides from 6 different side orders =
`\binom{6}{3}`

choose 2 flavor drinks from 7 different flavor drinks =
`\binom{7}{2}`

choose 3 ice cream from 9 different flavors of ice cream =
`\binom{9}{3}`

Total no of ways can a combo containing 2 burgers, 3 different sides, 2 different flavor drinks, and 3 ice cream flavors be made=

=
`\binom{6}{2}*\binom{6}{3}*\binom{7}{2}*\binom{9}{3}` ( Using combination )

=
`(6!)/((2!)(4!))*(6!)/((3!)(3!))*(7!)/((2!)(5!))*(9!)/((3!)(6!))`

=
`15*20*21*84`

= 529,200