A math instructor has 17 calculators in his desk Nine of the

A math instructor has 17 calculators in his desk. Nine of them are graphing calculators, 8 are programmable, and another 7 offer RPN (reverse Polish notation entry format). Of those with RPN, 4 do graphing and 3 are programmable. Only one calculator has all three features; 2 calculators are just basic four-bangers with none of the special features. How many programmable calculators does the instructor have that also do graphing?

Solution

N(total) = 17

N(Graphing) = 9

N(programmable) = 8

N(RPN) = 7

N(RPN and Graphing) = 4

N(RPN and Programming) = 3

N(RPN and Graphing and Programming) = 1

N(four bangers) = 2

Total Calculators = 17 - 2(removing four bangers) = 15

P(AUBUC)=P(A)+P(B)+P(C)- P(A?B)-P(A?C)- P(B?C)+P(A?B?C)

15 = 9 + 8 + 7 - N(RPN and Programming) - 4 - 3 +1

15 = 18 - N(RPN and Programming)

N(RPN and Programming) = 3

Hence there are three which can do both programming and RPN