The number of integers greater than 6,000 that can be formed, using the digits 3,5,6, 7and 8, without repetition, is :

$\mathrm{A}=\{3, 5, 6, 7, 8\}$

(Case i) four digit numbers begin with $6, 7, 8=3\times 4{\mathrm{P}}_3$

Case (ii) Number of 5 digit numbers using 3, 5, 6, 7, 8 = 5!

Total no. of numbers greater then 6000=

$\begin{array}{rcl} & =& \left(3\times 4{\mathrm{P}}_3\right)+5! \\ & =& 72+120\\ & =& 192 \\ & & \end{array}$