• Choice G
    The identification code will be in the following format: $$\underline{Digit_1}\ \underline{Letter_1}\ \underline{Letter_2}\ \underline{Letter_3}\ \underline{Letter_4}\ \underline{Digit_2}$$ \(\underline{Digit_1}\) and\(\underline{Digit_2}\) can be any digits from 0-9, while the letters can not be repeated from the 26 English alphabet. Thus the total number of possible codes is: $$10\cdot (26)\cdot (26)\cdot(25)\cdot(24)\cdot(23)\cdot 10$$ of which the number of codes with the fixed letters "MATH" $$ \underline{Digit_1}\ \underline{M}\ \underline{A} \ \underline{T} \ \underline{H}\ \underline{Digit_2} $$ is $$10\cdot 10$$ Therefore, the probability of randomly selecting such a code is: $$\frac{10\cdot 10}{10\cdot (26)\cdot (26)\cdot(25)\cdot(24)\cdot(23)\cdot 10}$$

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