in a bag there are infinitely many red white black balls which are identical if 10 balls are selected at random then the probability that the selection includes atleast one ball from each colour is Share with your friends Share 2 Shruti Tyagi answered this Dear Student, Given that there are three types of balls Red,white and black balls.we have to select 10 balls which will have combination of these 3 colorsHence lets say we selected (3R,3W,4B) balls which will end up to 10Hence we can have combination of (R,W,B) tuples adding upto 10like (1,1,8),(1,2,7) etc.So our problem reduced to finding the total number of solutions for following equationx+y+z=10where x,y,z>=0, since we need to select atleast 1 ball of each colorHere x is number of red balls, y white balls and z blue ballsThe total number of solutions for x+y+z=10 isCr-1n-1 [ using STARS and BARS combinatorics theorem]where n=10 and r =3(number of distinct colors)Hence total number of 10 balls can be selected such that atleast 1 ball of each color is selectedC3-110-1=C29=9!2!×7!=9×82=36Hence total 36 possible ways are there in which total number of 10 balls can be selected such that atleast 1 ball of each color is selectedTo find the probability =Number of possible ways to selecte 10 ballstotal number of waystotal number of ways =310 as each ball can be of any of the three colorsHence probability=36310=3659049 Regards, -6 View Full Answer Arnav answered this 1/10 -5
