Choose n random elements from every row of list of list

I have a list of list L as :

       [
         [1,2,3,4,5,6], 
         [10,20,30,40,50,60],
         [11,12,113,4,15,6],
        ]

Inner list are of same size. I want to choose n-random elements from every row of L and output it as same list of list.

I tried the following code:

import random
import math

len_f=len(L)
index=[i for i in range(len_f)]
RANDOM_INDEX=random.sample(index, 5))

I am stuck at this point that how can I use random index to get output from L.

The output for "2" random elements would be:

       [
         [1,6], 
         [10,60],
         [11,6],
        ]

If random function chose 1 and 6 as index.