MathematicsGarlands 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

A
$5! \times 6!$
B
$6! \times 6!$
C
$\frac{5!}{2!} \times 6!$
D
$2 (6! \times 6!)$

Solution:

6 yellow roses can be arranged in a circle in

(6 - 1)! = 5!

ways

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

As it is a garland,

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

Related content

Area of Square

Area of Isosceles Triangle

Pythagoras Theorem

Triangle Formulae

Perimeter of Triangle Formula

Area Formulae

Volume of Cone Formula

Matrices and Determinants_mathematics

Critical Points Solved Examples

Type of relations_mathematics