take a simple approach -
there is bag with red, blue and green balls each 2
R,R,B,B,G,G
p. of getting two red ball= 2/6*1/5= 1/15
now p. of getting same color ball=3*1/15
i.e. 1/15(R)+1/15(B)+1/15(G)=3*1/15
because question gives us pair and everytime 2 shoes will make a pair we can directly multiply
similarly with shoes,
p. of getting a pair of shoes= 2/20(first shoe)*1/19(second shoe)=1/190
now we have 10 pair of shoes so = 10*1/190= 1/19. (C)