Permutation-Combination
Aptitude

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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.

$36$

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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,

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

$= \textbf{21}$


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