There are 12 different flavors of ice-cream and triple decker cones are made in

Question

There are 12 different flavors of ice-cream and triple decker cones are made in homemade waffle cones. Having
chocolate ice-cream as the bottom scoop is different from having chocolate ice-cream as the top scoop.
How many possible ice-cream cones are there? How many cones with three different kinds of ice-cream are there? Counting the number of ice-cream is similar to counting the number of functions with the scoops as the domain and the flavors as the range. Which type of function can be found in (2) above? (check the one that applies)
One-to-one
Onto

Explanation / Answer

three decker cone is similar to 3 vacant places a) three vacant places with 12 different flavours of ice cream, when there is no restriction, can be filled in - 12*12*12 ways b) three vacant places with 12 different flavours of ice cream, when there all places have different flavours, can be filled in - 12*11*10 ways c) since we have all types of flavours included in our cases hence we can say that co-domain is equal to range & hence the function will be onto function

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