Ten members of a wedding party are lining up in a row for a photograph. (a) How
ID: 3851007 • Letter: T
Question
Ten members of a wedding party are lining up in a row for a photograph.
(a) How many ways are there for the wedding party to line up in which the bride is not next to the groom?
(b) How many ways are there for the wedding party to line up if the groom is not in the leftmost position?
(c) How many ways are there for the wedding party to line up if the groom is not at one end (i.e. in the leftmost or rightmost positions)?
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(b) How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?
Explanation / Answer
(a)
Total ways to line up 10 members = 10!
ways in which bride is next to groom = 9! x 2 (9! for 9 persons considering bride and groom as one entity and multiplied by 2 because bride and groom may interchange there place)
How many ways are there for the wedding party to line up in which the bride is not next to the groom = 10! - 2*9!
(b)
Groom at leftmost position = 9! (fix groom position, 9 persons left)
ways for the wedding party to line up if the groom is not in the leftmost position = 10! - 9!
(c)
ways for the wedding party to line up if the groom is not at one end (i.e. in the leftmost or rightmost positions) = 10! - 2*9!
(d)
90 integers
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