Question

The number of different garlands, that can be formed using $3$ flowers of first kind and $3$ flowers of second kind, is

• A. $60$
• B. $20$
• C. $4$
• D. $3$

Answer 1

The correct option is B $20$

There are $3$ flowers of first kind and $3$ flowers of second kind as well, but the garland is of circular shape

Refer image.

$a+b+c=3$

We know there are $3$ different flowers and we have to average them between $3$ people (lay a,b,b).

So we are average it as ${}^{n+x-1}{C}_{x-1}$ ways

$n=3$ $x=3$ substituting the value

${}^{(3+3)-1}{C}_{3-1}$= ${}^5{C}_2(3-1)!$

Since there are three flowers we can arrange it as $=\frac{5\times 4}{1\times 2}\times 2$

$(3-1)!ways=20$

(In circular object we can an average as similar objects in (n-1)!ways)

$B=20$