How many different four-digit numbers greater that 4000 can be formed from the digits {3, 4, 8, 9}, if : a. repetition is allowed b. repetition is not allowed.

a. 192

b. 18

Step-by-step explanation:

A four-digit numbers should start with 4, 8 or 9 to be larger than 4000

a. If repetition is allowed, there are 3 options for the 1st slot, 4 options for the 2nd slot, 4 options for the 3rd and last slots. Therefore a total of 3*4*4*4 = 192 possible combination.

b. If repetition is not allowed, there are 3 options for the 1st slot, 3 options for the 2nd slot, 2 options for the 3rd slot, 1 option for the last slot. This makes a total of 3*3*2*1 = 18 possible combinations.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x