The number of integers, greater than 7000 that can be formed, using the digits 3 , 5 , 6 , 7 , 8 without…

Case $1$ 

forming $4$ digit number,

When $7$ is at $1000\text{'}\text{s}$ place

$7 \_ \_ \_$,

So total number of ways will be $4\times 3\times 2=24$ ways,

Case $2$ 

forming $4$ digit number when $8$ is at $1000\text{'}\text{s}$ place 

$8 \_ \_ \_$,

So total number of ways will be $4\times 3\times 2=24$ ways,

Case $3$ 

forming $5$ digit number,

So total number of ways will be $5!=120$ ways,

Now adding all the cases we get, $120+24+24=168$ ways.