Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability junior

Problem

Seven cards each containing one of the following letters C, B, T, A, E, M and H are placed in a hat. Each letter is used only once. Stu will pull four cards out at random and without replacement. What is the probability that Stu pulls out M, A, T, H in this order? Express your answer as a common fraction.
Solution
The probability that Stu pulls the M out first is 1/7. The probability that he then pulls the A out next is 1/6, since there are now 6 letter remaining. Continuing in this way, the probability that he pulls out T next is 1/5 and the probability that H then follows is 1/4. Therefore, the probability that he pulls out M, A, T, H in this order is .
Final answer
\frac{1}{840}