I'm studying for a statistics exam, and I'm stuck with a few combination\permutation questions. Here are the questions (with answers):
In a bucket there are: 4 blue balls, 5 white balls, and 6 red balls. We choose 3 balls randomly:
a) How many choosing possibilities are there if all 3 balls are different in color? (Answer: 120)
b) How many choosing possibilities are there if at least 2 of the 3 balls are identical in color? (Answer: 335)
In a certain language, the alphabet consists of 22 letters. How many different words consisiting of 6 characters can we form, considering each word has to contain at least 2 identical characters? (Answer: 59658544)
From a group of 7 men and 8 women, we want to choose an expedition that consists of 4 people and contains an equal number of men and women. In this expedition there are 3 jobs: leader, treasurer, and spokesman of the expedition. The fourth person of the expedition doesn't have a defined job. How many different choosing possibilites do we have in order to achieve such an expedition, if every person had the qualifications to hold any of the jobs? (Answer: 14112)
The answers were provided with the questions, however without explanation. Can someone please explain to me in detail how to get to the answers?
Thanks a lot in advance.