7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.*A) 7!/2B) 7!/3C) 7!/4D) 7!/5E) 7!/6
Question
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.*A) 7!/2B) 7!/3C) 7!/4D) 7!/5E) 7!/6
Solution
The total number of arrangements for 7 people is 7! (7 factorial), which means 7654321 = 5040 arrangements.
However, we have two conditions here: A will not sit to the left of F and F will not sit to the left of E. This means that A, F, and E will always sit in the order of A-F-E. We can consider these three people as one unit.
So now we have 5 units (A-F-E, B, C, D, G) to arrange, which can be done in 5! = 120 ways.
But within the A-F-E unit, they can arrange themselves in 3! = 6 ways.
So the total number of arrangements considering the conditions is 5!*3! = 720.
Therefore, none of the options A) 7!/2, B) 7!/3, C) 7!/4, D) 7!/5, E) 7!/6 match the correct answer.
Similar Questions
A group of 6 friends goes to the movies, but when they get into the theater there are only 3 seats left in the front row. In how many ways can the friends fill the seats in the front row?
Six friends go to a movie theater. In how many different ways can they sit together in a row of 6 empty seats?There are ways can they sit together in a row of 6 empty seats.
ad the given information carefully and answer the problems given below:Eight persons A, B, C, D, E, F, G, and H are sitting around a circular table but do not needs to be sitting in the same arrangement. Five of them are facing inner while others are facing outward.E is third to the right of C. F sits third to the left of E. Three persons sit between F and B. G sits third to the right of F who is not facing the centre. D sits third to the right of A, who is not facing the centre.Who sits just between F and A?
Select the correct answerStudy the following information carefully and answer the question given below.Some persons are sitting in a row adjacent to each other facing north direction. Only four persons sit between F and G. C sits seventh to the left of G. Only four persons sit to the left of C. Only four persons sit between sit between C and P. More than two persons sit between F and P. E sits at extreme right end. Q sits third to the left of E. H sits seventh from one of the end but sits to the immediate right of F. Only three persons sit between H are R, who sits to the left of Q. How many persons sit in the row?Options242019Can’t be determined18
Directions: Study the following information and answer the given question. Six friends A, B, C, D and F seating in a circle facing towards center.E is the left of D.C seats between A and B and F is between E and A.Who is sitting immediate left of B?CDF None of these
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.