Answer: A. [tex]\dfrac{6}{203}[/tex]
Step-by-step explanation:
Given : Jason bought 10 of the 30 raffle tickets for a drawing.
i.e. Total tickets = 30
Also, Number of prizes = 3
The total number of combinations of getting 3 prizes out of 30 tickets = [tex]^{30}C_3[/tex]
The number of combinations of getting 3 prizes out of 10 tickets =[tex]^{10}C_3[/tex]
Then, the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away will be :
[tex]\dfrac{{^{30}C_3}}{^{10}C_3}[/tex]
[tex]=\dfrac{\dfrac{10!}{3!7!}}{\dfrac{30!}{3!27!}}=\dfrac{120}{4060}=\dfrac{6}{203}[/tex]
Hence, the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away is [tex]\dfrac{6}{203}[/tex] .
Hence, the correct answer is A. 6/203.
