Question: a.) A bagel shop has onion bagels, egg bagels, sesame seed bagels and plain bagels. How many ways are there to choose twelve bagels with at least one of each kind? This question is similar to P.373 Example 4 and P.379 #9.

b.) Find the next larger permutation in lexicographic order after the permutation 42837651? This problem is similar to P.383 Example 2 and P.386 #3.