Question 56 Answer and Explanation _ACT December 2016 Form 74H Math Section

56. At Wafer Technologies, identification codes each consist of the following sequence: 1 digit, 4 letters, 1 digit. For any 1 code, the digits (0–9) may be the same, but the letters, each from the English alphabet, must all be different. Which of the following expressions gives the probability that a randomly selected identification code contains the word MATH, spelled correctly?

F. $\frac{{10}^{2}}{{10}^{2}({26}^{4})}$

G. $\frac{{10}^{2}}{{10}^{2}(26)(25)(24)(23)}$

H. $\frac{{10}^{2}}{10(9)(26)(25)(24)(23)}$

J. $\frac{{10}^{2}(4)(3)(2)(1)}{{10}^{2}({26}^{4})}$

K. $\frac{{10}^{2}(4)(3)(2)(1)}{10(26)(25)(24)(23)}$

Answer and Explanation

Your Answer is

Correct Answer is G

Explanation

This six-digit code has a total of 10²×26×25×24×23 possibilities. A total of 10²possibilities including MATH. Therefore choose G.