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10 Sep 2019, 10:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:19) correct
36%
(02:09)
wrong
based on 182
sessions
History
Date
Time
Result
Not Attempted Yet
A teacher wishes to seat 5 boys and 3 girls in a row at a bench. In how many ways can the teacher seat the boys and the girls so that all the girls do not sit together?
(A) 720
(B) 2160
(C) 4032
(D) 18000
(E) 36000
(A) 720
(B) 2160
(C) 4032
(D) 18000
(E) 36000
10 Sep 2019, 11:13
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No. of ways in which all the 3 girls do not sit together= Total no of ways in which 5 boys and 3 girls can sit - No. of ways in which all the three girls sit together.
Total no. of ways in which 5 boys and 3 girls can sit = 8! = 40320
Total no. of ways in which all the 3 girls sit together
Consider three girls as one entity
Now we have 5 boys and one girls group to sit
Ways of arranging 6 people= 6! = 720
The three girls can be arranged in themselves in 3! ways= 6 ways
Total no. of ways in which three girls sit together= 720*6 = 4320
No. of ways in which all the 3 girls do not sit together= 40320-4320
36000
IMO answer (E)
Total no. of ways in which 5 boys and 3 girls can sit = 8! = 40320
Total no. of ways in which all the 3 girls sit together
Consider three girls as one entity
Now we have 5 boys and one girls group to sit
Ways of arranging 6 people= 6! = 720
The three girls can be arranged in themselves in 3! ways= 6 ways
Total no. of ways in which three girls sit together= 720*6 = 4320
No. of ways in which all the 3 girls do not sit together= 40320-4320
36000
IMO answer (E)
General Discussion
30 Sep 2020, 23:11
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Given
To Find
Approach and Working Out
Correct Answer: Option E
- • A teacher wishes to seat 5 boys and 3 girls in a row at a bench.
To Find
- • The number of ways can the teacher seat the boys and the girls so that all the girls do not sit together.
Approach and Working Out
- • Total number of ways to see 5 boys and 3 girls = 8!
• The ways in which all the girls seat together = 6! * 3!
• The answer is the difference between these two.
- o = 8! – 6! × 3!
o = 6! × (8 ×7 – 6)
o = 6! × 50
o = 36000
Correct Answer: Option E
