How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?
A. 12
B. 144
C. 288
D. 1,400
E. 5,040
The OA is B .
I didn't know how to use the permutations here. I need your help experts.
How many different ways are there to arrange a group
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi VJesus12,
We're asked to arrange a group of 3 adults and 4 children in 7 seats with adults in the first, third, and seventh seats. We're asked for the number of arrangements possible. This question is a variation on a standard Permutation question. To solve it, we have to go from space to space and keep track of the 'options' available for each (noting that once we place a person, there is one fewer person available for the next equivalent spot).
For the 1st spot, there are 3 options
For the 2nd spot, there are 4 options
For the 3rd spot, there are 2 options
For the 4th spot, there are 3 options
For the 5th spot, there are 2 options
For the 6th spot, there are 1 options
For the 7th spot, there are 1 options
Total arrangements = (3)(4)(2)(3)(2)(1)(1) = 144 possible arrangments
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're asked to arrange a group of 3 adults and 4 children in 7 seats with adults in the first, third, and seventh seats. We're asked for the number of arrangements possible. This question is a variation on a standard Permutation question. To solve it, we have to go from space to space and keep track of the 'options' available for each (noting that once we place a person, there is one fewer person available for the next equivalent spot).
For the 1st spot, there are 3 options
For the 2nd spot, there are 4 options
For the 3rd spot, there are 2 options
For the 4th spot, there are 3 options
For the 5th spot, there are 2 options
For the 6th spot, there are 1 options
For the 7th spot, there are 1 options
Total arrangements = (3)(4)(2)(3)(2)(1)(1) = 144 possible arrangments
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
VJesus12 wrote:How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?
A. 12
B. 144
C. 288
D. 1,400
E. 5,040
The OA is B .
I didn't know how to use the permutations here. I need your help experts.
The 3 adults can be arranged in 3! = 6 ways, and the 4 children can be arranged in 4! = 24 ways, so the total number of arrangements is 6 x 24 = 144.
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
3 adults can be seated in 1st, 3rd and 7th position in 3! ways.VJesus12 wrote:How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?
A. 12
B. 144
C. 288
D. 1,400
E. 5,040
The OA is B .
I didn't know how to use the permutations here. I need your help experts.
The remaining 4 positions are occupied by the remaining 4 people in 4! ways.
Hence the total number of seating arrangements is 3!*4! = 144 ways.