QR Probability Qeustion

[299678]

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

Correct answer is 110, but my calculation is 108

 

[TexasOMFS]

To answer this question, remember that only one vacancy must be reserved for female however this does not mean you can't have MORE than one female. So the possibilities are, 2 males/1 female, 2 females/1 male, and 3 females.
2 males/1 female: 5!/(3!2!)*5=50
2 females/1 male: 5!/(3!2!)*5=50
3 females: 5*4*3/3*2=10
50 + 50 + 10 = 110
The reason I divided by the numbers that I did is because if you choose first Jane then Carly, this is essentially the same as choosing Carly first then Jane.

 

[299678]

Could you explain this in more detail? Why you multiply for each x 5?

 

[redchesus]

In the first option: 5!/(3!2!) is how many ways you can pick 2 males out of 5 (combination)

multiplied by 5, which is the number of ways you can pick 1 female out of 5 (in actuality, it is 5!/(4!1!) but it should be fairly obvious without calculations that it is 5)

and same thing, for the other 2 options

 

[sfoksn]

i think redchesus meant permutation

 

[redchesus]

i think redchesus meant permutation

no, because order doesn't matter here

if it were permutation it would be 5!/3! = 20 and not 5!/(3!2!) = 10