Aptitude 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,

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

$= \textbf{21}$