The case of =2 is: c 41/c 61* c 31/c 51= 6/15.
The case of =3 is: white, red, red; Red and white: 2 * c 21/c 61* c42/c52 = 6/15.
The case of =4 is: white, white, red, red; White red, white red; Red, white, white and red 3* C22/C62 * 1 = 3/ 15
The average probability is12/15+18/15+12/15 =14/5.