Answer:
The total number of ways the person holding ticket 47 wins one of the prizes = 941,094
Step-by-step explanation:
Given - 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).
To find - How many ways are there to award the prizes if it satisfies the given conditions. The person holding ticket 47 wins one of the prizes.
Proof -
The order of selection is important because 1st selection is grand prize , 2nd selection is second prize and so on . So , we use permutation for this question
Now,
As The person holding ticket 47 wins one of the prizes and other 3 prizes are also given to the remaining 99 persons who got chosen
So,
The number of ways = 1* ⁹⁹P₃
=
=
=
= 99*98*97
= 941,094
∴ we get
Total number of ways the person holding ticket 47 wins one of the prizes = 941,094