How to do this ques?

#1

lg (n!) = ………………

O(n)

O(lg n)

O(n^2)

O(n lg n)

#2

the answer would be O(nlgn) to get the answer you need to expand n!

#3

i tried that but was unable to obtain the soln

#4

lg(n!) = lg(n) + lg(n-1) + lg(n-2) …
after removing the insignificant term we can write the 2nd, 3rd and so on terms as lg(n) only and since we will have n such terms we can write nlgn