How many ways are there to distribute seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear?
I'm having trouble with this problem because it is not the same as the first part that asks how many ways if the apples and pears are identical.
I have tried several different approaches that have proven to be unsuccessful and I could really use some help. Thanks in advance!
The total number of ways to distribute six different pears to three people is $3^6$. Using inclusion/exclusion, the number of ways to do it in which no person remains pearless is $$3^6-3\times2^6+3\times1^6\ .$$ Distributing seven different apples too makes the total number of ways to do it $$3^7(3^6-3\times2^6+3)\ .$$