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Examveda

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. 20

C. 21

D. 36

Answer: Option C

Solution(By Examveda Team)

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
= 21

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