The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is
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4 flowers which are always together can be considered as one SET,
Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland.
Which means, 5 things to be arranged in a garland.
(5-1)!
And the SET of flowers can arrange themselves within each other in 4! ways.
Therefore
(5-1)!*(4!)
But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference.
Therefore
(5-1)! * (4!)/ 2
= 288.
or
Simply :- (5-1)! * 4!/2
So Total value will be 288
Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland.
Which means, 5 things to be arranged in a garland.
(5-1)!
And the SET of flowers can arrange themselves within each other in 4! ways.
Therefore
(5-1)!*(4!)
But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference.
Therefore
(5-1)! * (4!)/ 2
= 288.
or
Simply :- (5-1)! * 4!/2
So Total value will be 288
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