i. Given

= 30 × 29

= 870

ii. Given

We know that:

11! = 11 × 10 × 9 × … × 1

10! = 10 × 9 × 8 × … × 1

9! = 9 × 8 × 7 × … × 1

Putting these values, we get,

= 110 – 10

Hence,

iii. We have to find LCM of 6!, 7!, and 8!

We can write as,

= 8! = 8 × 7 × 6!

= 7! = 7 × 6!

= 6! = 6!

Therefore,

L.C.M (6!, 7!, 8!) = LCM [8 × 7 × 6!, 7 × 6!, 6! ]

= 8 × 7 × 6!

Hence, LCM is 8!