Assessment: Permutation and Combination

A restaurant has 3 soups and 5 salads. How many different soup-and-salad combos are possible?

Evaluate 4!.

In how many ways can a gold and silver medal be awarded to 2 of 6 runners?

In how many ways can a committee of 4 be chosen from 9 people?

How many distinct arrangements are there of the letters in "MISSISSIPPI" (11 letters: M=1, I=4, S=4, P=2)?

In how many distinct ways can 7 people be seated around a circular table?

A lottery draws 6 numbers from 49, without regard to order. Should the number of possible outcomes be computed using permutations or combinations?

A quality control inspector needs the probability of randomly selecting 2 defective items from a batch, given the total counts of defective and non-defective items. Which counting technique underlies this calculation?

All 6 letters of a 6-letter word (all distinct) can be rearranged 6! ways, but 2 of those arrangements must be excluded (they spell offensive words). How many valid arrangements remain?

A committee of 3 must be chosen from 10 people, but 2 specific people refuse to serve together. How many valid committees are there? (Total committees minus those including both conflicting people.)