First we deal with the 4 digit numbers: [] [] [] []
As for the first digit, only 5, 7 ,8 and 9 can be used, as utilizing 3 will lead to the number being smaller than 4000 thus does not satisfy the condition of >4000.
In order to find out how many 4 digit numbers that are >4000, we use 4P1x4P1x3P1x2P1=96 numbers.
(We pick one number from 5,7,8,9 for 1st digit, and at the 2nd digit, 3 can now be used hence there will still be 4 numbers to pick on for the 2nd digit, we have used 2 numbers so far, thus the 3rd digit having 3 to pick from, the last digit having 2 numbers to pick from. That explains for the eqn above)
Now we move on to five digit numbers. It is fairly straight forward since all five digit numbers are >4000, thus we can just use 5P5=120
120+96=216
note that when dealing with situations where the ORDER does matter eg. numbers and letters, we use nPr instead of nCr
hope this helps!
