Question

the number of integers greater than 6000 that can be formed by using the number 3,5,6,7 without repetition​

Answer 1

We can have either 4 digit or 5 digit number.

First consider 4 digit number.

We can take 6,7,8 at the thousandth place.

The next three places can be filled in 4C3⋅3! way.

So we get 72 such numbers

For 5 digit number, we can choose them in 5! ways(120).

So total no of such numbers are 72+120=192.

hope this helps you dear

Answer 2

Answer: We can have either 4 digit or 5 digit number.

First consider 4 digit number.

We can take 6,7,8 at the thousandth place.

The next three places can be filled in   $^{4}C_{3}$ ⋅ 3! way.

So we get 72 such numbers

For 5 digit number, we can choose them in 5! ways(120).

So total no of such numbers are 72+120=192