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.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)