Question

If $n$ is number of necklaces which can be formed using $17$ identical pearls and two identical diamonds and similarly $m$ is number of necklaces which can be formed using $17$ identical pearls and different diamonds, then

• A. $n=9$
• B. $m=18$
• C. $n=18$
• D. $m=9$

Answer 1

Answer: (A), (D)

$n=9$
$m=9$

Problem is same as dividing $17$ identical things in two groups.
$\therefore n=\frac{17+1}{2}=9$
There is no effect if two diamonds are different as necklace can be flipped over. Hence, $n=m=9$.