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Five women and four men have volunteered to serve for one hour each to answer phones...

Five women and four men have volunteered to serve for one hour each to answer phones during a nine-hour telethon.
a. How many schedules are possible if there are no restrictions on the order of the schedule?
b. How many schedules are possible if two people came in the same car and would like to have con- secutive hours?

how to solve for the first answer to be 9!

andhow to solve to get the second answer to be 8!

math   Statistics-And-Probability   
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Answer #1

a) for no restriction: number of possible schedules =N(9 choice for 1st person, 8 choices for 2nd except 1st one, 7 choices for 3rd except first 2 selected and so on ..) =9*8*7*6*5*4*3*2*1 =9!

b)

here for two people to be consecutive , we need to treat them as a unit, and other seven as seperate individuals,

therefore total number of unit which needs to be arranged =8

number of ways to arrange them =8!

(Note: here the 2 person who are considered to be 1 unit can be arraged in 2 ways, as AB or BA , therefore number of ways should be 2*8!)

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