If the last four people each took 400 jelly beans, they took a total of 4*400 = <<4*400=1600>>1600 jelly beans.
The first six people each took twice as many jelly beans as each of the last four people took, meaning each of them took 2*400 = <<2*400=800>>800 jelly beans.
The total number of jelly beans the first six people took is 800*6 = <<800*6=4800>>4800 jelly beans.
Together, all 10 people took together 4800+1600 = <<4800+1600=6400>>6400 jelly beans.
If there were 8000 jelly beans in a certain barrel, the number of jelly beans that remained is 8000-6400= <<8000-6400=1600>>1600
#### 1600