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# The no. of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are not separated is?

$\begin{array}{1 1} 4!4! \\ \frac{8!}{4!} \\ 288 \\ 5!.4! \end{array}$

Toolbox:
• No. of ways in which $n$ different things can be arranged in a circle = $(n-1)!$
Since a garland is in circular shape, circular permutation is used.
4 flowers are to be together.
$\therefore$ they are to be considered to be one.
Hence there are 5 different type of flowers.
They can be arranged in a circle in $4!$ ways.
But these 4 flowers that are together can be arranged among themselves in $4!$ ways.
$\therefore$ The required no. of arrangements $= 4!.4!$

edited Dec 20, 2013