Probability doubt
Can you please help me understand the below question and it’s explanation from GMATONTHEGO:
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There are 5 students standing in a line. In how many ways can ten students arrange in a line such that two students Daniel and Chelsea want to stand next to each other?
- 60
- 120
- 180
- 240
- 360
First tie the students: total number of ways 5!
Two students can interchange in 2! ways.
Total number of ways 5! x 2! = 240
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I believe question says that 5 students need to be arranged in a line with two specific students always together. If that’s the case, shouldn’t answer be 4! X 2! = 48 as we are considering two students as one unit. Hence total 4 students to be arranged and can arrange two students in 2! ways. Please let me know what I am doing wrong?
Thanks,
Nikunj
Hi niksdoon,
The question has some problems. In first line it mentioned as 5 students, then the question asks, in how many ways ten students be arranged ?
Even if we consider 5 students arranging in a line, the explanation and answer is not correct.
Because even if we consider total arrangements of 5 people still it would be 5!= 120, so answer has to be less than that.
What you did is exactly right. answer has to be 48.
Again, I apologize since the question is from GMATonthego and thanks once again bringing this for our notice.
