Chapter 6 - Section 6.5 - Generalized Permutations and Combinations - Exercises - Page 433: 37

$210$

We are trying to count the number of ways to consume three mangos, two papayas, and two kiwis. This is equivalent to the number of permutations of seven fruits, with the three mangos indistinguishable from each other, the two papayas indistinguishable from each other, and the two kiwis indistinguishable from each other. By Theorem 3 on page 428, the number of ways to do this is: $\frac{7!}{3!2!2!}$ $=\frac{1*2*3*4*5*6*7}{1*2*3*1*2*1*2}$ $=\frac{4*5*6*7}{2*2}$ $=210$