Angelica C.

asked • 05/22/16

Leslie bought 5 flavors of ice cream and 3 toppings. She will choose 2 flavors and L topping for a sundae. How many different sundaes can she make?

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Andrew M.

Logic tells me I can make 30 combinations:
Calling my flavors  a, b, c, d, e
Calling my toppings 1, 2, 3
 
With flavor a I can make
ab1   ac1  ad1   ae1
ab2   ac2  ad2   ae2
ab3   ac3  ad3   ae3
 
That is 12 combinations using ice cream flavor a.
As long as ab is the same as ba for flavor combinations,
I can do the same thing to get 9 combinations
using flavor b with c,d,e and topping 1,2,3
 
Then 6 using flavor c with d,e and topping 1,2,4
 
Then finally 3 using flavor d,e with 1,2,3
 
At this point we can't go any further because
flavor e has already been combined with each
of the other 4 flavors and toppings.
 
I know there are formulas and such for permutations and
combinations and such, but those aren't my best area.
 
Still, 30 combinations of 2 and 1 from this scenario is it.
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05/22/16

1 Expert Answer

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Arthur D. answered • 05/22/16

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5 flavors of ice cream and 3 toppings
choose 2 flavors and 1 topping
first choose 2 flavors of ice cream
use the formula n!/(r!)(n-r)! where n=5 and r=2
(5!)/(2!)(5-2)!
(5!)/(2!)(3!)
(5*4*3*2*1)/(2*1)(3*2*1)
simplifying
(5*4)/(2*1)
20/2
10 combinations of 2 flavors
each of the 10 combinations can be combined with 1 of the 3 toppings
10*3=30
you are correct, however, you need to know the formula in case the numbers involved are very large !!
 
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