There are four questions related to this: how many number of ways are there to award the prizes if:
a) There are no restrictions? If k unalike awards are there for n people and no person can get more than one prize then there are: This leads to 100 × 99 × 98 × 97 = 94109400100 × 99 × 98 × 97 = 94109400 ways in your case where n=100 k=4.
b)The person holding ticket 47 wins the grand prize? After handing out the grand prize there are k=3 different rewards left for n = 99 persons. Apply the same formula. Answer: 941094941094
c) The person holding ticket 47 wins one of the prizes? 4 times case because there are 4 likelihoods when it comes to the rewards that can be won by person 47. Answer: 37643763764376
d) The person holding ticket 47 does not win a prize? k=4 and n =99.
Person 4747 is left out. Answer: 9034502490345024
e) The person holding ticket 19 and 47 both wins prize? First gave out a
prize to 47. There are 4 possibilities. Then give out a prize
to 19. There are 3 likelihoods. Then the other prizes are gave
out: k=2 and n=98. Lastly you come to 4 × 3 × 98 × 97 =1140724
× 3 × 98 × 97 = 114072 possibilities.
