1. 10 people are seated to a 10 people spot in a row in the movies. a) b) How ma
ID: 2922434 • Letter: 1
Question
1. 10 people are seated to a 10 people spot in a row in the movies. a) b) How many different ways can they sit? Suppose the 10 are five married couples who all want to sit with their spouses. How many ways can they sit? Suppose that Adam (one of the husbands) and Suzie (one of the wives, not married to Adam) cannot stand each other. How many different sittings are there p will still sit with their spouses.) c) ossible? (Each d) Mary and Allice are best friends and want to sit together (each will still sit with her husband). How many different sittings are there possible? e) How would your answers for (a-d) change if it was a round table seating? Explain why. ( am not looking for exact answers. Just comment whether your answers will increase or decrease)Explanation / Answer
a) number of different ways =first position have 10 choice*second 9* third 8*.... =10*9*8*7*..1 =10! =3628800
b)number of ways =arrangement of 5 couples in order *every couple has 2 internal arragement where they can switch left or right =5! *25 =3840
c) number of ways Adam and Suzie always sit together =(as adam and suzie couple are together; we need to arrnage 4 married couple and each couple have two internal arrangements) =4!*24 =384
hence number of ways Adam and Suzie does not sit together=3840-384=3456
d)total number of ways Mary and Alice will sit together =4!*24 = 384
e) for round table as there is left to right and right to left arrangement both looks the same; therefore number of arrangeemnts will decrease when considering round table seating.
please revert for any clarifiation required.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.