SOLUTION: An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice

Algebra ->  Permutations -> SOLUTION: An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice       Log On


   

Question 308851: An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice cream is always scooped before the toppings are added. In how many distinct ways can the serving be assembled? Also if the customer wants three different flovors of ice cream how many choices does he have?
Answer by stanbon(75887) About Me  (Show Source):
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An ice cream shoppe carries five kinds of ice cream. They also have three kinds of toppings. One serving consists of three scoops of ice cream and three scoops of toppings.The ice cream is always scooped before the toppings are added.
In how many distinct ways can the serving be assembled?
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ways to assemble the 3 scoops of ice cream:
5 ways to pick the 1st scoop
5 ways to pick the 2nd scoop
5 ways to pick the 3rd scoop
Total ways: 5^3 = 125
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ways to assemple the 3 scoops of toppings:
3*3*3 = 27
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Total assemblies: 125*27 = 3375
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Also if the customer wants three different flavors of ice cream how many choices does he have?
5*4*3 = 60 choices
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Cheers,
Stan H.