Probability Theory 1- Counting Methods (Permutations and Combinations)

Tell me if any problems or errors thanks http://www.geocities.com/burnyboy2004/

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Education

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• probability
• theory
• counting
• methods
• combinations
• permutations
• york
• university
• maths
• mathematics
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[kdontoh]

1. In how many ways can 9 women and 9 men stand in a line for a picture? In how many ways can these people stand in line if the order must be woman, man, woman, man, ... ?

[burny1]

@kdontoh Well the first part it doesnt matter on gender so just 18!. For the second part there are 9! ways of each of the genders being arranged and for each of the male arrangements there are 9! ways for the women to arrange so i would say 9!*9!. If in doubt write it out! except in this case i suppose ha.

[WellConditionedChimp]

I have a question for the example you give @ 2:27. In combinations, the order doesn't matter. When picking 2 red marbles, the order doesn't matter. So why wouldn't you divide by 2!?

[burny1]

@WellConditionedChimp Thats a good point. We are not using the colours in the working out we are just using the number of balls. So we want the number of ways you can pick 2 balls from 8 and 2 from 5 with no regards for colour its just there to give us some numbers to work with, this is my understanding. I hope i made sense

[abosalem5513]

i think the answer in example 2 is like that

2! * 3! * 2! = 24 ways

[burny1]

@abosalem5513 thanks i changed the answer and out of 2000 views its wierd that you are the first to notice. thanks for that

[malcolmbryant]

Note on terminology: Your lottery question asks "What [are] the odds" but you give the answer in the form "the probability is..."

Odds = the ratio of possible failures to possible successes; probability = the ratio of possible successes to all possible outcomes.

[WellConditionedChimp]

@burny1 when I did the problem again, the 2! would be present in the denominator of the numerator and the denominator of the denominator, so they would cancel out. That gives the same answer that you gave on the video. I'm taking the gre soon, so this video was helpful. I cut math class often in middle and high school, so it's a long, winding road to competency. Thanks for filling in some pot holes.

[abosalem5513]

you are welcome friend

[middleeaster]

Very nice m8... You will be a good teacher one day :P