33. Consider strings of eight English letters. Count
(d)
strings that start with a vowel, letters cannot be repeated
(g) strings that start with x and contain at least one vowel; letters can be repeated
= number of strings that start with x  number of strings that start with x but do not have a vowel
47. Consider the problem of forming a row of 6 people, including a bride and a groom, for picture taking.
Count the number of ways a row can formed if
(a) the bride and groom must be next to each other.
(b) the bride and groom must not be next to each other
= total # of ways to seat 6 people
 the count in part (a)
(c)
# of ways in which the bride is to the left of the groom
10/11/11
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46.
Seating of six out of 10 people including the bride and the groom for a
picture.
(a)
The bride must be in the picture.
Two subtasks: pick a place to seat the bride;
pick people to seat the remaining five positions
Total ways = 6* (9*8*7*6*5)
47 (c) Alternative counting technique
First form a line with the other 4 people in 4! ways
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 Fall '11
 Boppana
 Natural number, Count von Count, bride

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