Kenneth Rosen Edition 7 Exercise 6.5 Question 37 (Page No. 433)

Question

A student has three mangos, two papayas, and two kiwi fruits. If the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed?

Answer 1

Here we have given student has 3 mangoes,2 papayas and 2 kiwi fruits.

so in total he has (3+2+2) =7 fruits.

let all the fruits to be eaten.if he eat one fruit each day then it will take 7 days to complete this process.

so this becomes a permutation problem because order of eating of fruits matter.

so according to one of popular permutation type where , n=7, n1(mangoes)=3,  n2(papayas)=2,  n3(kiwi)=2.

so number of ways =7!/(3!2!2!) =210