Answer to Question #345139 in Statistics and Probability for fitre

Question

 You are taking a test to see if you have supernatural abilities that involves a deck of five cards that each show one of five symbols (which we will call (A, B, C, D, E)). The cards are placed in a sequence so that each card appears exactly once; no repeats are allowed. Your job is to guess the correct sequence. (a) How many different sequences are possible? (b) What is the probability that you guess all five cards in the sequence correctly? (c) What is the probability that the letters AB occur consecutively and in that order some where in the sequence?

Answer 1

a) There are 5! = 120 possible sequences.

b) the probability that you guess all five cards in the sequence correctly is 1/120

c) You can replace AB with a single new symbol such as Q. You now have 4 characters C, D, E and Q which gives you 4!=24 possible combinations. So, the probability that the letters AB occur consecutively and in that order some where in the sequence is 24/120=0.2