There are ten pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is

• 105/323
  total chhances=20c4
  10c1*18c2+10c2/20c4
• 10 years agoHelpfull: Yes(6) No(0)
• Case 1 A pair in 2nd draw = 1*1/19
  Case 2 A pair in 3rd draw = 1*18/19*2/18
  case 3 A pair in 4th draw = 1*18/19*16/18*3/17
  
  Ans = sum of all 3 = 99/323
• 10 years agoHelpfull: Yes(4) No(0)
• The way we can select no pair of socks is:
  Select one sock from 20 sock in the first pick. In the second draw exclude the pair of the first selected sock and pick from the remaining 18 socks and so on.
  = 20C1 * 18C1 * 16C1 * 14C1/4!
  So required probability: 1 - ((20C1 * 18C1 * 16C1 * 14C1/4!)/20C4) = 99/323
• 10 years agoHelpfull: Yes(4) No(0)