Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

Step-by-step solution

White balls =7 , black Balls =3 , Total Balls =10 Total number of ways to place all these balls in a row aligned & = 10! 7! 3! = 10 9 8 7! 7! 3 2 1 & n=120 aligned Now, The number of ways in which no two black balls put together is equal to the number of ways of choosing 3 places marked places of eight places. - W - W - W - W - W - W - W - This can be done in ^8 C ₃ ways. aligned & Required probability = ^8 C₃ 120 = 8! 3!5!120 & P= 8 7 6 5! 3 2 5! 120 = 7 15 aligned