(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is (""). Show that the number of integer partitions (of any size) with at most n narts and with largest part of

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(a) Show that the number of paths from (0,0) to (n, m) taking
steps of size (0,1) or (1,0) is ("m").
(b) Show that the number of integer partitions (of any size) with at most n parts and with largest part of
size at most m equals ("+").
Transcribed Image Text:(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is ("m"). (b) Show that the number of integer partitions (of any size) with at most n parts and with largest part of size at most m equals ("+").
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