There are 210 ways that he can consume fruits. This can determined using the concept of factorial in mathematics.
Factorial, in mathematics, the product of all positive int or numbers less than or equal to a given positive int or number and denoted by that integer and an interjection point. therefore, factorial seven is written seven!, meaning one × 2 × 3 × 4 × 5 × six × seven.
Factorial zero is defined as equal to one.
Here, we have given the student has three mangoes, two papayas and two kiwi fruits.
so in total he has (3 plus 2 plus 2) =7 fruits.
Let all the fruits be eaten. If he eats one fruit each day then it will take seven days to complete this process.
So according to one popular permutation type where , n=7, n1(mangoes)=3, n2(papayas)=2, n3(kiwi)=2.
Using factorial, number of ways =7!/(3!2!2!) =210
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