In an identification code the first place is filled from (4) letters the second from (5) digits and the third from (2) symbols. How many codes can be formed?

Correct answer: (40) codes

The direct answer is option A: 40 codes. The code has three ordered positions: the first position has 4 choices, the second has 5 choices, and the third has 2 choices. Since one choice is made at every position and the choices are independent, multiply them: \(4\times5\times2=40\). Option A is correct. Option B, 20, leaves out one factor and counts only \(5\times2\) or an equivalent incomplete calculation. Option C, 11, adds the numbers instead of counting combinations of choices; addition is not suitable when every position must be filled. Option D, 80, is twice the correct product and gives no valid interpretation of the stated choices. The order of positions matters because a letter choice in the first position is different from the same type of choice in another position. A reliable method is to draw three boxes and write 4, 5, and 2 above them, then multiply the numbers above the boxes.