Unformatted text preview: 5. How many onto functions are there from a set of 5 elements to a set of 3 elements? 6. How many ways can you return n hats to n people so that (a) Exactly one person gets their original hat back? (b) At least two people get their original hats back? 7. Show that n ! = ( n ) D n + ( n 1 ) D n-1 + · · · + ( n n ) D 8. Show that the sequence D n (the number of derrangements of n objects) satisﬁes the recurrence relation D n = ( n-1)( D n-1 + D n-2 ) 9. Find a generating function for the number of partitions of n that have only even-sized pieces. 10. (Tricky but Cute) Show that for any positive integers n,k , the number of partitions of n that have k parts is the same as the number of partitions of n that have k as their largest part....
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
- Summer '08