How Many 4-Digit Permutations Greater Than 5364 Can Be Formed?

[Daaniyaal]

Homework Statement

8. Using the digits 1, 2, 3, 5, 7, 8 how many 4 digit numbers greater than 5,364 could be constructed if:
a) Repetition of the digits is allowed?
b) Repetition of the digits is not allowed?

Homework Equations

The Attempt at a Solution

for part a:
2*6*6*6 (for 8 and 7 as the first digit)
+
1*4*2*3 (for 5 as the first digit)

But it is incorrect :(

Correct answer is 552 for part a and 150 for part b

 

[CAF123]

For part a), consider 3 cases: The first digit > 5, the first two digits being 5 and 3, the first digit being 5.

If the first digit is 5 and the second 3, then this puts a restriction on the last two. If the first digit is 5 and the second > 3, then there is no restriction on the last two. This is what your answer does not take into consideration.