20 couples and 45 single people are queuing up at the movies

20 couples and 45 single people are queuing up at the movies waiting for tickets. The queue is very strict in that each person must stand behind the other (except of course the first person in line). How many wyas might these 85 people be arranged in the line, if the couples stay together in the line (but still one behind the other). Oerder matters - order in the line, order within a couple, etc.

Give the final answer in the form of a mathematical equation involving addition, subtraction, multiplication, division, exponentiation, and/or factorial.

Solution

Dear Student Thank you for using Chegg !! Given there are 20 couples and 45 single people in the queue Since the couples have to be to gether (one behind the other) in the queue Hence let us consider them one entity which can be arranged in 2 factorial ways No of ways of arrangement of 65 entities ( single + Couples) = factorial 65 Total Number of ways of arrangement = 65! X 2! (Final Answer) 1.64953E+91