There are 30 cards. Each card has a single number written on it, such that all the integers from 1 to 30 are represented in the cards. Two cards (which have numbers a and b written on them) are arbitrarily chosen, and are removed from the pack. The above two cards are replaced with a single card, on which the number (ab + a + b) is written. This constitutes one operation. After 29 such operations, what will be the number written on the sole surviving card?1) 31! − 1 2) 15 × 31 3) 30! − 1 4) 31! + (15 × 31) 5) 30! + (15 × 31) − 1

1) 1
2) 2
3) 3
4) 4
5) 5

• for 1,2 y=5 =(3!-1)
  for 1,2,3 y = 23 = (4!-1)
  similarly here 31!-1
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