Question

How many ways $10$ different beads can be threads for making a garland where as $4$ special beads never remain separate?

Answer 1

Given total beads=10
​4 special beads never remain separate, considering them as a single bead, we get, 1+6=7 beads

So, the number of ways arranging 7 beads in circular path $=(7-1)!=6!$ ways and
again $4$ beads arranging themselves in $4!$ ways.

So, total arrangement's $=\left(6\right)!\times 4!$

$=720\times 24$

$=17280$ ways.