Bunuel wrote:
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?
A. 3
B. 6
C. 9
D. 18
E. 36
Take the task of seating the 6 students and break it into
stages.
NOTE: Since the boys must sit in seats 1, 3 and 5, the girls must sit in seats 2, 4 and 6
Stage 1: Select a boy to sit in seat #1
We can choose any of the 3 boys, so we can complete stage 1 in
3 ways
Stage 2: Select a girl to sit in seat #2
We can choose any of the 3 girls, so we can complete stage 2 in
3 ways
Stage 3: Select a boy to sit in seat #3
There are 2 boys remaining to be seated, so we can complete stage 3 in
2 ways
Stage 4: Select a girl to sit in seat #4
There are 2 girls remaining to be seated, so we can complete stage 4 in
2 ways
Stage 5: Select a boy to sit in seat #5
There is 1 boy remaining to be seated, so we can complete stage 5 in
1 way
Stage 6: Select a girl to sit in seat #6
There is 1 girl remaining to be seated, so we can complete stage 6 in
1 way
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus seat all 6 children) in
(3)(3)(2)(2)(1)(1) ways (= 36 ways)
Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
RELATED VIDEOS