Question

You write 4 different names on index cards. You shuffle the cards and then lay them out in a row. What is the probability that they will come out in alphabetical order? Express your answer as a fraction in simplest form.

Answer 1

We are assuming that the initials are different. Let them be A, B, C, D.

Clearly ABCD is the only possible outcome where the letters are in alphabetical order.

The total number the outcomes, is the number of permutations of these 4 letters.

The first letter can be any of the 4, the second, any of the 3 left (after having picked the first one), the third any of the 2 left (after picking the second one), and the fourth one is only 1 possibility.

So the total number of outcomes (permutations) is 4*3*2*1=24


P(alphabetical order)=1/24




Answer: 1/24