Consider two letters Q and Y and two numbers 5 and 8. There 24 passwords of length 4 that uses these characters without repetitions. Show that when a password is chosen at random from this set, the probability of getting passwords in which Q comes earlier than both the numbers (written from left to right) is 1 3 .

The probability of selecting a password such that Q comes earlier than both the numbers is .

Step-by-step explanation:

The options to form a password of length 4 are: Q, Y, 5 and 8.

The total number of passwords that can be formed is, 4! = 24.

The condition applied is: Q comes earlier than both the numbers.

The sample space satisfying this condition is:

S = {QY58, QY85, YQ58, YQ85, Q58Y, Q85Y, Q5Y8, Q8Y5}

  = 8 possible passwords.

The probability of selecting a password such that Q comes earlier than both the numbers is:

Thus, the probability of selecting a password such that Q comes earlier than both the numbers is .

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is