Answered

On a famous episode of Star Trek, Captain Kirk and the gang played a card game called Phisbin. This problem is about another game, called Frisbin. The object of Frisbin is to throw three Frisbees at three different-sized bins that are set up on the ground about 20 feet away from the player. If a Frisbee lands in the largest bin, the player scores 1 point. If a Frisbee lands in the medium-sized bin, the player scores 5 points. If a Frisbee lands in the smallest bin, the player scores 10 points. Kirk McCoy is playing the game. If all three of his Frisbees land in bins, how many different total scores can he make?

Answer :

jepessoa

Answer:

10 different possible scores

Step-by-step explanation:

the total possible scoring combinations are:

large bin (1)   medium bin (5)     small bin (10)    score

3                             0                             0                   3    

2                             1                              0                   7

2                             0                             1                    12

1                              2                             0                   11

1                              0                             2                   21

1                              1                              1                    16

0                             3                             0                   15

0                             2                             1                    20

0                             1                              2                   25

0                             0                             3                   30

 

fichoh

Using the principle of combination, the number of different total scores that can be made is 10.

Using the combination relation which includes repetition :

  • [tex] \binom{n + k - 1}{k} [/tex]
  • n = number of Frisbee = 3
  • k = number of bins = 3

Substituting the values into the formula :

[tex] \binom{3 + 3 - 1}{3} = \binom{5}{3} [/tex]

Using the combination formula :

[tex]nCk = \frac{n!}{(n-k)!k!}[/tex]

[tex]5C3 = \frac{5!}{(5-3)!3!}[/tex]

[tex]5C3 = \frac{5!}{2!3!}[/tex]

[tex]5C3 = \frac{5 \times 4}{2} = \frac{20}{2} = 10[/tex]

The number of different total scores that he can make is 10.

Learn more :https://brainly.com/question/19299862

Other Questions