Question

No. of ways of selecting $3$ consecutive objects out of $15$ objects (distinct) placed around a circle is

• A. ${}^{15}{C}_r$
• B. ${}^{14}{C}_3$
• C. $13$
• D. $15$

Answer 1

The correct option is D $15$

Number of Ways of selecting 3 objects out of 15 circular oriented objects
lets number them $x_1,x_2,..x_{15}$
we need to select consecutively 3 objects
So first object can some $x_k$ then other would $x_k,x_{k+1}$ for $k\le 13$
other ways would be $(x_{14},x_{15},x_1)$ and $(x_{15},x_1,x_2)$
so total selection will $13+2$ ways so $15$ ways