Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. Six boxes are numbered $1,2,3,4,5$ and $6$. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. Find the total number of ways of placing the balls.
 ✖ A. $15$ ✖ B. $29$ ✔ C. $21$ ✖ D. $36$

Solution:
Option(C) is correct

If there is 1 black ball, it can be placed in 6 ways.

If there are 2 black balls, they can be placed in 5 ways (in $1,2 ; 2,3 ; 3,4 ; 4,5$ and $5,6$) and so on.

If there are 6 black balls, they can be placed in 1 way.

The total number of ways of placing the balls is,

$1+2+3+4+5+6$

$= \textbf{21}$