A. The total numebr of ways or permutaion selecting three balls from the bag without replacement is 720.
B. The probability of getteing a ball or selecting a ball marked with number five is [tex]\frac{1}{5}[/tex].
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
The formula for the permutation is
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
n is the total number of objects
r is the total number of selected students
[tex]^{n} P_{r}[/tex] is the total number of permuations
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
According to the given question.
Total number of balls in a bag = 10
A. Three balls are selected at a randow.
Since, repetition is not allowed or replacement is not allowed.
So, the number of ways selecting the first ball is 10
Number of ways selectiong the second ball is (10-1)
Number of ways selecting the third ball is (9-1)
Therefore,
The total number of ways or permutation selecting three balls from a bag
= [tex]^{10} P_{3}[/tex]
[tex]= \frac{10!}{(10-3)!}[/tex]
[tex]= \frac{10!}{7!}[/tex]
[tex]=\frac{10\times 9\times 8\times 7!}{7!}[/tex]
[tex]= 10\times 9\times 8[/tex]
[tex]= 720[/tex] ways
Hence, the total numebr of ways or permutaion selecting three balls from the bag without replacement is 720.
B.
Total number of ball in a bag = 10
Total number of ball in a bag marked with 5 = 1
Thereofre,
the probability of selecting a ball marked with number 5
= [tex]\frac{total\ number\ of \ balls\ marked\ with \ number\ five\ }{total\ number\ of\ balls\ in\ a \ bag}[/tex]
[tex]= \frac{1}{5}[/tex]
Hence, the probability of getteing a ball or selecting a ball marked with number five is [tex]\frac{1}{5}[/tex].
Find out more information about proability and permutaion here:
https://brainly.com/question/14368656
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