Question

The number of ways that a garland can be made out of $6$ red and $4$ white roses of different sizes, so that all the white roses come together is

• A. $8640$
• B. $4320$
• C. $720$
• D. $360$

Answer 1

The correct option is A $8640$

With all white roses coming together , total numbers.
can be considered as $6$ red $+1$ single $=7$ elements.
$\therefore$Total numbers of ways of arranging in garland is
$\frac{(n-1)!}{2}=\frac{(7-1)!}{2}=\frac{6!}{2}$
No. of ways of arranging white roses is $4!$
$\therefore$ Total arrangement $=\frac{6!}{2}\times 4!=8640$