See in the question they have asked for number of strings of length at least 3
so
Consecutive a's >=3 in the strings
Case 1: consecutive a's= 3 (aaa)
We have 5 possible alphabets A, B, C, D, E
so to choose 3 consecutive places out of 6 we have 4 possible ways
case 1.1 _ _ _| _ _ _
Total 1*1*1*4*5*5 =100 strings we place consecutive a's 1,2 3 positions
case 1.2 _| _ _ _ |_ _
Total 4*1*1*1*4*5 = 80 strings if we place consecutive a's on 2,3,4 position
Case 1.3 _ _| _ _ _ |_
Total 5*4*1*1*1*4 = 80strings If we place consecutive a's in 3,4,5, position
case 1.4 _ _ _| _ _ _|
Total 5*5*4*1*1*1 = 100 strings if we place a's on 4,5,6 position
Finally for case 1 we get 100+80+80+100= 360 strings
Now let's count similarly for other cases
case 2: consecutive a's= 4 (aaaa)
Now if we choose 4 consecutive positions out if 6 we get 3 possible ways
case 2.1 _ _ _ _ _ |_
Total 1*1*1*1*4 *5= 20 strings if we place a at 1,2,3,4, position
case 2.2 _ |_ _ _ _ |_
Total 4*1*1*1*1*4= 16 strings if we place a at 2,3,4,5 position
case 2.3 _ _ |_ _ _ _|
Total 5*4*1*1*1*1= 20 strings if we place a at 3,4,5,6 position
From case 2 we get 20+16+20= 56 strings
Case 3 : for 5 consecutive a's (aaaaa)
if we choose 5 consecutive position out of 6 we can do this in 2 ways
Case 3.1 _ _ _ _ _ |_
Total 1*1*1*1*1*4= 4 strings we get if we place a's on position 1,2,3,4,5
Case 3.2 _ l_ _ _ _ _|
Total 4*1*1*1*1 strings we get if we place a's on position 2,3,4,5,6
From case 3 we get total 2*4= 8 strings
Case 4: we have all 6 a's at all 6 position we can do this in only 1 way (aaaaaa)
1*1*1*1*1*1= 1 strings
In total if count strings all from case 1,case 2,case3 and case 4 we gate
360+56+8+1= 425 strings total which are of length 6 ans contain at least 3 consecutive a's
