Problem: a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Rationale: "1 of 5 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 5 candidates for the math dep . , which gives as 5 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 5 * 45 = 225 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans e"
annotated_formula: multiply(multiply(10, 3), 5)