Question help thank you! Six students (Dave, Michael, Ann, Joe, Jane, Bill) are
ID: 3292546 • Letter: Q
Question
Question help thank you!
Six students (Dave, Michael, Ann, Joe, Jane, Bill) are attending a lecture in a classroom with 10 seats. The seats are in a single row as follows All valid seating arrangements are equally likely. By valid seating arrangement we mean that all students have to sit down in a seat and students can not share seats. Here is an example of a valid seating arrangement:
Dave - B, Michael - A, Ann - E, Joe - I, Jane - H, Bill - F
(a) How many seating arrangements are there? Note that who sits where matters.
(b) What is the probability of the seating arrangement Dave - A, Michael - C, Ann - D, Joe - H, Jane - I, Bill - J?
(c) What is the probability that Dave sits in seat A?
(d) What is the probability that seats A, C, D, H, I and J are occupied?
(e) What is the probability that seat A is occupied?
(f) What is the probability that Dave sits in A and Michael sits in C or Dave sits in A and Bill sits in F?
Explanation / Answer
a) 5 seats can selected(10c5) and arranged them seleves(5!) =(10C5)*5!
= 30240
b) single seating arrangement(ACDHIJ) of total is = 1/30240
c) If Dave sits in A,(one place occupied) remaining 9 places for 4 persons there are (9C4)*4!
. P(Dave sits in A) = (9C4)*4!/30240
= 3024/30240
= 1/10
d) There are 6! ways to fill in A,C,D,H,I, and J.
P(A,C,D,H,I, and J are occupied) = 6!/30240
= 1/42
e) If seat A is occupied, there are 9 places and 4 persons (9C4)*4! P(A is occupied)
= (9C4)*4!/30240
= 3024/30240
= 1/10
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