A box contains 8 red and x number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is 7 15 then number of green balls is _______

Step-by-step solution

Let R = 8 be the number of red balls and G = x be the number of green balls. The total number of balls is then N = R + G = 8 + x . The total number of ways to draw 3 balls is 8 + x 3 = (8 + x)(7 + x)(6 + x) 6 . The number of ways to draw exactly 3 red balls is 8 3 = 56 . Given that the probability of drawing 3 red balls is 7 15 , the equation becomes: 7 15 = 56 (8 + x)(7 + x)(6 + x) 6 = 336 (8 + x)(7 + x)(6 + x) . Rearranging gives: (8 + x)(7 + x)(6 + x) = 336 15 7 = 720 . The product of three consecutive integers