Answer:
62.5%
Step-by-step explanation:
p is either even or row.
IF P IS EVEN
If even then p(p+1)(p+2) will be always be divisible by 8. p and p+2 are even numbers an at least one of those two numbers is divisible by 4.
let say that p/2=a and (p+2)/2=b, then a is even or b is b is even (b=a+1, therefore one of those two numbers must be even), so if b is divisible by 2 then (p+2) is divisible by 4, or if a is divisible by 2 then p is divisible by 4.
p(p+1)(p+2) = 2*a*(p+1)*2*b
since a or b are divisible by 2 then p(p+1)(p+2) is divisible by 8
IF P IS ROW
If p is row, then p+2 is also row, and p(p+2) is also row (and row numbers are never divisible by 8), so p(p+1)(p+2) is divisible if and only if (p+1) is divisible by 8. The list of p between 1 and 96 where (p+1) is divisible by 8 is: 7,15,23,31,39,47,55,63,71,79,87,95. A total of 12 numbers.
IN CONCLUSION
for all even numbers, between 1 and 96, p(p+1)(p+2) is divisible by 8. there are 43 even numbers.
For all the row numbers, between 1 and 96, just (p+1) divisible by 8 will be divisible by 8 . There are 12 numbers like that.
[tex] \frac{46+12}{96} = 0.625 = 62.5 \%[/tex]
