Respuesta :
Answer: a) 3628800, b) 720.
Step-by-step explanation:
Since we have given that
Number of men = 6
Number of women = 4
So, Total number of persons = 6+4 =10
(a) How many different rankings are possible?
Using "fundamental theorem of counting", we get that
there are [tex]10!=3628800[/tex] different ranking which is possible.
(b) If only 3 students are selected at random, how many different rankings are possible in this case? Use a tree diagram to find the list of all possible rankings in this case.
Number of ranking possible if only 3 students are selected is solved with the help of "Permutations":
[tex]^{10}P_3=720[/tex]
Hence, a) 3628800, b) 720.
A) there are 3,628,800 different rankings, and B) there are 12,096,000 different rankings.
Given that a class in probability theory consists of 6 men and 4 women, and an exam is given and the students are ranked according to their performance knowing their gender but without knowing their names, assuming that students obtains a different score, to determine (A ) how many different rankings are possible, and B) if only 3 students are selected at random, how many different rankings are possible in this case, the following calculations should be performed:
- 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = X
- 90 x 56 x 30 x 12 x 2 = X
- 5040 x 30 x 24 = X
- 3,628,800 = X
- 10/3 = 3,333
- 3.3333 x 3628800 = X
- 12,096,000 = X
Therefore, A) there are 3,628,800 different rankings, and B) there are 12,096,000 different rankings.
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