A ice cream seller sells five flavours of ice creams. How many combinations of 3 scoops of cones are possible. Hint repition of flavours is allowed
you can choose each scoop 5 ways, so 5^3=125
To find the number of combinations, we can use the concept of combination with repetition.
In this case, since there are 5 flavors of ice cream and we are choosing 3 scoops with repetition allowed, it can be thought of as selecting 3 items from a set of 5 (with the possibility of selecting the same item multiple times).
The formula to compute combinations with repetition is (n + r - 1) choose r, where n is the number of options and r is the number of selections.
Plugging in the values, we have (5 + 3 - 1) choose 3, which simplifies to 7 choose 3.
To calculate this, we use the combination formula:
n choose r = n! / (r! * (n-r)!)
So, 7 choose 3 = 7! / (3! * (7-3)!)
Calculating further:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
(7-3)! = 4 * 3 * 2 * 1 = 24
Substituting these values into the formula:
7 choose 3 = 5040 / (6 * 24) = 5040 / 144 = 35
Hence, there are 35 possible combinations of 3 scoops of ice cream cones from 5 flavors when repetition is allowed.