One hundred tickets, numbered 1,2,3, ,100, are sold to 100 different people for a drawing. four different prizes are awarded, including a grand prize (a trip to tahiti).

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.  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.  37643763764376 

d) The person holding ticket 47 does not win a prize? k=4 and n =99. Person 4747 is left out.  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.

i used to know how to do this in 7th but i forget easily

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i can answer this question sweetie!

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