Mathematics: Baskin-robbins offers 31 different flavors of ice cream. one of its items is a bowl consisting of three scoops of ice cream, each a different flavor. how many such bowls are possible?

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Baskin-robbins offers 31 different flavors of - id313816284, RealSavage4Life

Ответ:

quarrella

10.01.2022

Mathematics

The answer is the number of subsets with cardinality 3 that we can extract from a set with cardinality 31.

The answer is the binomial coefficient

$\displaystyle\binom{n}{k}=\dfrac{n!}{k!(n-k)!}$

Where the factorial is defined as

$n!=n(n-1)(n-2)(n-3)\ldots 3\cdot 2$

So, your answer is

$\displaystyle\binom{31}{3}=\dfrac{31!}{3!\;28!}=\dfrac{31\cdot 30\cdot 29\cdot 28\ldots 2}{3\cdot 2\cdot 28\ldots 2}=\dfrac{31\cdot 30\cdot 29}{3\cdot 2}=31\cdot29\cdot5=4495$

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Baskin-robbins offers 31 different flavors of ice cream. one of its items is a bowl consisting of three scoops of ice cream, each a different flavor. how many such bowls are possible?

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