Respuesta :
[tex]|\Omega|=4\cdot3\cdot2=24\\|A|=1\cdot3\cdot2+1\cdot3\cdot2=12\\\\P(A)=\dfrac{12}{24}=\dfrac{1}{2}[/tex]
The probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].
What is probability?
Probability is the chance that something will happen, or how likely it is that an event will occur.
What is the formula for the probability?
The formula for the probability is
[tex]P(E) = \frac{number \ of \ favorable \ outcomes }{Total\ number\ of\ outcomes}[/tex]
Where,
P(E) is the probability of any event.
What is permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
What is the formula for the permutation?
The formula for the permutation is given by
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the permutation
n is the total number of objects
r is the total number of objects to be selected
According to the given question.
We have total four numbers 2, 4, 6, 7.
So,
The total number of three digits can be formed using these four numbers = [tex]^{4} P_{3}[/tex] = [tex]\frac{4!}{(4-3)!} =\frac{4\times 3\times 2\times 1}{1}[/tex][tex]=24[/tex]
Now, for making three digits number which are greater than 600 by using 2, 4, 6, 7 without repetition is given by
Number of ways for filling hundred place is 2 (either 6 or 7).
Number of ways for filling tens place is 3 (if 6 is placed at hundred place then remaining numbers are 7, 2, 4 and if 7 is place at hundred place then remaining numbers are 6, 2, 4).
Number of ways for filling one place is 2(because only 2 number are left).
Therefore, the total numbers of three digits can be formed by using these numbers 2, 4, 6, and 7
[tex]= 2\times 3\times 2\\=12[/tex]
So,
the probability that the number is formed greater than 600
= [tex]\frac{total\ three\ digits\ numbers\ which\ are \ formed \ by\ using\ 1,\ 2, \ 3, \ and\ 4\ which\ are\ greater\ than\ 600 }{Total \ three\ digits\ numbers\ formed\ by \ using \ 1,\ 2,\ 3,\ and \ 4}[/tex]
[tex]= \frac{12}{24}[/tex]
[tex]= \frac{1}{2}[/tex]
Therefore, the probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].
Find out more information about probability and permutation here:
https://brainly.com/question/14767366
#SPJ2
