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25 Jul 2018, 21:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:17) correct
20%
(01:32)
wrong
based on 286
sessions
History
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Not Attempted Yet
A mathematics department has 5 members. The department must send a team of 2 members to a conference. If there is one pair of members who refuse to attend together, how many possible pairs of department members can be chosen?
A. 14
B. 9
C. 7
D. 5
E. 3
A. 14
B. 9
C. 7
D. 5
E. 3
25 Jul 2018, 21:34
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Updated on: 25 Jul 2018, 23:05
Originally posted by EgmatQuantExpert on 25 Jul 2018, 22:51.
Last edited by EgmatQuantExpert on 25 Jul 2018, 23:05, edited 1 time in total.
Last edited by EgmatQuantExpert on 25 Jul 2018, 23:05, edited 1 time in total.
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Solution
Given:
- • A mathematics department has 5 members.
• The department must send a team of 2 members to a conference.
• One pair of members refuse to attend together.
To find:
- • How many possible pairs of department members can be chosen?
Approach and Working:
Let department members are: A, B, C, D, and E and A and B refuse to attend the conference together.
Hence, Total cases:
- • Select A as select 1 member other than B
- o So, we have to select 1 more member out of 3 members.
o Number of ways= \(^3c_1\)=3
- • Select B as select 1 member other than A
- o So, we have to select 1 more member out of 3 members.
o Number of ways= \(^3c_1\)=3
- • Do not select either of A or B
- o So, we have to select 2 more members out of 3 members.
o Number of ways= \(^3c_2\)=3
Hence, total ways=9
Hence, the correct answer is option B.
Answer: B
