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
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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