12 candles are selected at random from a large collection of white, red, green and yellow candles. The number of candles

Question

12 candles are selected at random from a large collection of white, red, green and yellow candles. The number of candles of each colour is unlimited. Find the probability that the selection contains at least one marble of each colour?  
    
  a. 34/91  
  b. 23/31  
  c. 36/91  
  d. 33/91  
  e. 1/4  
    
  need a good and easy approach

Vijaya Lakshmi K · Answer

Hello Varun,

W|R|G|Y
There are 3 lines or partitions and 12 marbles. These 3 partitions divide the 12 marbles in 4 groups (W, R, G and Y).
1. When there is at least 1 marble in each group
Total number of ways= n-1Cr-1= 11C3 {n=12 and r=4}

2. When there are no restrictions
Total number of ways= n+r-1Cr-1= 15C3
Probability= 11C3/15C3= 11*10*9/15*14*13= 33/91

Therefore, the answer is option D

Hope this helps.