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A certain university will select 1 of 7 candidates eligible [#permalink]

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05 Jan 2008, 09:39

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A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

N=7C1*2C10=7*45=315 we use 2C10 rather than 2P10 because "2 of 10 candidates eligible to fill 2 identical positions in the computer science department" _________________

well , I could get the OA, but can someone please explain what is the significance of this statement "If none of the candidates is eligible for a position in both departments",. I thoght we were finding combinations of eligible candidates!
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well , I could get the OA, but can someone please explain what is the significance of this statement "If none of the candidates is eligible for a position in both departments",. I thoght we were finding combinations of eligible candidates!

it means that the candidates of science department can not be eligible for the math department. Two groups are saperate, no overlap
_________________

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

well , I could get the OA, but can someone please explain what is the significance of this statement "If none of the candidates is eligible for a position in both departments",. I thoght we were finding combinations of eligible candidates!

it means that the candidates of science department can not be eligible for the math department. Two groups are saperate, no overlap

got it! had got confused with the wording. thanks!
_________________

-Underline your question. It takes only a few seconds! -Search before you post.

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42 B. 70 C. 140 D. 165 E. 315

7/1!*6! --> 7 * 10!/2!*8! --> 5*9 --> 5*9*7 =315

----------------------------------------------------------------------- Can you please explain why is it 7C1 ?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42 B. 70 C. 140 D. 165 E. 315

7/1!*6! --> 7 * 10!/2!*8! --> 5*9 --> 5*9*7 =315

----------------------------------------------------------------------- Can you please explain why is it 7C1 ?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42 B. 70 C. 140 D. 165 E. 315

As "none of the candidates is eligible for a position in both departments" then we have 7+10=17 candidates.

\(C^1_7*C^2_{10}=7*45=315\): \(C^1_7\) - choosing 1 from 7 and \(C^2_{10}\) choosing 2 from 10 when order doesn't matter as 2 positions in computer science department are identical (XY is the same as YX).