Lighting 10 LEDs Randomly

Good Morning

I want to light 10 LEDs randomly. More specifically, turn on one LED at random, leave it on, then turn on a second LED at random, leave it on, and so forth until a line of 10 LEDs are all lit.

My circuit is an Arduino Uno with a ten segment bar-graph (DIP, NTE3115) connected to DigPins 4 thru 13, they are called LEDa thru LEDj.

I can get to 10 LEDs to light individually in a random pattern in a sketch that is an expanded version of Light Blink. The overall sketch is wordy and sloppy but it works well enough.

Any other tips would be appeciated.

Below is a the section of the sketch dealing with random blinking

while(count<300)                 //start Random_Pattern and run 300 times
  { 
   if(randnum==1)                         //see if randnum is 1
  {
   digitalWrite(LEDa, HIGH);          //if randnum is 1 turn on LEDa
   delay (randelay);                      //leave LEDa on for random time
  }
  else
  {
   digitalWrite(LEDa, LOW);          //if randnum is not 1 turn off LEDa
  }
  if(randnum==2)                         //see if randnum is 2
  {
    digitalWrite(LEDb, 1);             //if randnum is 2 turn on LEDb /Same as HIGH/
    delay (randelay);                    //leave LEDb on for random time
  }    
  else
  {
   digitalWrite(LEDb, 0);               //if randnum is not 2 turn LEDb off
  }
    
// A LARGE SECTION OF THE SKETCH WAS OMMITED HERE TO KEEP THE FORUM POST SMALLER//

  if(randnum==10){                      //see if randnum is 10
  digitalWrite(LEDj, 1);                //if randnum is 10 turn LEDj on
  delay(randelay);                       //keep LEDj on for random time
  }
  else{
  digitalWrite(LEDj,0);                 //if randnum is not 10 turn LEDj off
  }  
  
  digitalWrite(LEDa,0);                 //next ten lines keep two lights from being lit
  digitalWrite(LEDb,0);                 //at the same time
  digitalWrite(LEDc,0);
  digitalWrite(LEDd,0);
  digitalWrite(LEDe,0);                 // DISABLE FOR A BETTER EFFECT
  digitalWrite(LEDf,0);
  digitalWrite(LEDg,0);
  digitalWrite(LEDh,0);
  digitalWrite(LEDi,0);
  digitalWrite(LEDj,0);  
  randnum = random(1,11);               //change randnum
  randelay = random(5,40);              //change random delay number
  count++;

There is a nice algorithm for selecting random elements from a set with minimum effort.
repeat
select a random element from the array.
copy the last element in the selected place.
make the size of array one smaller

Small sketch to get the idea.(not tested)

int array = { 0,1,2,3,4,5,6,7,8,9 };

void setup()
{
  Serial.begin(115200);

  for (int size = 10; size > 0; size--)
  {
    int x = random(size);
    Serial.println( array[x] );  // process led x
    array[x] = array[size];   // copy last element to place x as x is used,
  }
}
void loop(){};