Question

Suppose that four men and four women will be randomly lined up, from left to right, with all possible orderings of these eight people being equally likely. What is the probability that the men will be in alphabetical order, from left to right, and at the same time the women will also be in alphabetical order, from left to right

Answer 1

P = 1 / 40320 or P = 2.48*10⁻⁵

Explanation:

The total number of outcomes To is:

To = 8! To = 8*7*6*5*4*3*2

To = 40320

Of all these outcomes there is only one proper outcome, therefore the probability of having all men and women in alphabetical order is:

P = 1 / 40320 or P = 2.48*10⁻⁵