QR Question

[Orgodox]

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In how many ways can 10 candidates be elected for 3 vacancies (5 male and 5 female) of which one vacancy is reserved for a female?

They say the first can be filled by and of the 5 women. the next 2 is 9C2=36

So shouldnt you now multiply the two because there are 36 ways 2 can be filled and that can be multiplied by any of the first 5 women

so 36X5 but they say its 36+5 ???????? and answer is 41

any thoughts?

 

[klutzy1987]

In how many ways can 10 candidates be elected for 3 vacancies (5 male and 5 female) of which one vacancy is reserved for a female?

They say the first can be filled by and of the 5 women. the next 2 is 9C2=36

So shouldnt you now multiply the two because there are 36 ways 2 can be filled and that can be multiplied by any of the first 5 women

so 36X5 but they say its 36+5 ???????? and answer is 41

any thoughts?

Can one female be differentiated from another.

 

[HoangDDS]

The question is kinda confusing. I understood it like this (please correct me if I am wrong), so there is 10 people (5 males and 5 females) for 3 vaccine. But one vaccine is reserved for female only. So how many ways can we arrange the combination of these 3 vaccines to 10 people? -- is that what it is asking?

If so, I got 50. But I don't think I did it right. This is how I went about it:

Since there is only 2 vaccine for all 10 people, I did :
10! / (10-2!)(2!) = 45 combinations

And since 1 vaccine is only for female, there can only be 5 combination of that.

so 45+ 5 = 50. --- I was working on this for 10mins and I still don't get how they got 41. What does it mean when you posted 9C2 = 36?

 

[Mstoothlady2012]

In how many ways can 10 candidates be elected for 3 vacancies (5 male and 5 female) of which one vacancy is reserved for a female?

They say the first can be filled by and of the 5 women. the next 2 is 9C2=36

So shouldnt you now multiply the two because there are 36 ways 2 can be filled and that can be multiplied by any of the first 5 women

so 36X5 but they say its 36+5 ???????? and answer is 41

any thoughts?

I believe when you have independent probability, you multiply. When the two scenarios are dependent on each other, you add them!

 

[Orgodox]

Can one female be differentiated from another.

I assume so

 

[Danny289]

where is streetwolf? 😡

😉

 

[PooyaH]

In how many ways can 10 candidates be elected for 3 vacancies (5 male and 5 female) of which one vacancy is reserved for a female?

They say the first can be filled by and of the 5 women. the next 2 is 9C2=36

So shouldnt you now multiply the two because there are 36 ways 2 can be filled and that can be multiplied by any of the first 5 women

so 36X5 but they say its 36+5 ???????? and answer is 41

any thoughts?

You did it right!!! But you have to add 5 to 36 because in every scenario, you are reserving 1 spot for a woman!!! so the rest of the combination is going to be beween 9 ppl in which it could be either 2 women or 2 men. So you have 5 women that you have to put in one vacancy for each combination! I'm not sure if I'm doing a good job at explaining this, but I'm sure streetwolf is better at it lol

 

[Mstoothlady2012]

like I said before the first part of the answer you found is NOT independent of the second half of the answer. Hence, you add those instead of multiplying.

Like the common probability question, what is the probability that you will toss head both times you flip a coin? If you get head first time, does this mean you won't get head second time or vice versa? No they are not related at all!! There fore you multiply 1/2 x 1/2 = 1/4

The 5 spots that you found are with the overall answer. The 5 spots you found correspond to the other 36 spots that you got. Does this make sense??

 

[Streetwolf]

This was in another thread a while back. The answer key is wrong. The answer should be 110.

The best way to do this, and also the easiest to understand, is to start with the total number of 3 person groups. This is just (10 C 3) = 120. Now the question says one spot is reserved for a woman. This is a fancy way of saying that at least one woman is in the group. So to do that, you take all the possible cases and subtract the number of cases that have only men. Then you're left with all the cases with at least 1 woman.

All men = (5 C 3) * (5 C 0) <-- choose 3 men out of 5, choose 0 women out of 5

This equals 10.

So 120 - 10 = 110, your answer.

 

[Orgodox]

Thanks streetwolf I was waitin for your reply. Yea I thought it was an error. I wrote crack but so hope no one else reported it yet and keep adding to my total money.