in part a, you need 3 distinct students, cuz 1 person cant get both the first and second prizes, so for first prize, its 10, for second, its 9 (cuz a kid already got first) and for third place its 8 (2 kids already got and award) therefore 10x 8 x9 or 10P3
however, in part b, if a child has already got an award, they could still get another one, eg, i could get an award for both physics and chem. so, for the physics prize, its 10 students, for chem, its also 10 (physics kid could get chem too) and then for maths, its also 10 (kids who got phys or chem can also get math) so, its 10x10x10=1000