Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

# Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

1. A
$5!×6!$
2. B
$6!×6!$
3. C
$\frac{5!}{2!}×6!$
4. D
$2\left(6!×6!\right)$

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### Solution:

6 yellow roses can be arranged in a circle in $\left(6-1\right)!=5!$  ways

6 gaps can be filled by red roses in $6!$  ways

As it is a garland,

Number of ways $=\frac{1}{2}×5!×6!=\frac{5!}{2}×6!$

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