John borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?.  Choices
A) 12 / 91 B) 3 / 15 C) 12 / 15 D) 33 / 91 E) 3 / 91

Rationale: since jake owns 3 of the boots , the subset from which the 4 boots should be chosen are the 12 boots not owned by jake from the universe of 15 . the first boot can be one of the 12 from the 15 with probability 12 / 15 . the second boot can be one of the 11 from the 14 remaining with probability 11 / 14 . the third boot can be one of the 10 from the 13 remaining with probability 10 / 13 . the fourth boot can be one of the 9 from the 12 remaining with probability 9 / 12 . the total probability will be 12 / 15 × 11 / 14 × 10 / 13 × 9 / 12 . on cancellation , this comes to 33 / 91 . thus , the answer is d - 33 / 91
Answer: D