Step-by-step explanation:
remember, a probability is always desired cases over total possible cases.
the class has 10+15 = 25 students.
and 5 of them will be picked as representatives to the school board.
how many total possibilities do we have ?
since picked students can be picked only once, and the sequence of the 5 picked students in the group does not matter, we have a combination without repetition :
C(25, 5) = 25! / (5! × (25-5)!) = 25! / (5! × 20!) =
= 25×24×23×22×21 / (5×4×3×2) =
= 5×1×23×22×21 = 53,130 possible outcomes.
how many desired outcomes ?
that would be how many options we have to pick 2 out of 10 and 3 out of 15 :
C(10,2) × C(15,3) = 10! / (2 × 8!) × 15! / (3! × 12!) =
= 10×9/2 × 15×14×13/(3×2) =
= 5×9 × 5×7×13 = 20,475 desired outcomes
and the probability is
20475 / 53130 = 4095 / 10626 = 1365 / 3542 = 195 / 506
= 0.385375494... ≈ 0.39
