It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places.
It is required to seat 4 boys and 3 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
Answer/Solution
144
Steps/Work
Total number of candidates = 4 + 3 = 7. In the row of 7 positions, the even places are 2nd, 4th, 6th .
Now, number of even places = 3.
Number of girls to occupy the even places = 3.
Even places can be filled = P (3, 3) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144
ANSWER:B
Now, number of even places = 3.
Number of girls to occupy the even places = 3.
Even places can be filled = P (3, 3) ways.
Number of boys = 4.
The remaining 4 places can be filled by 4 boys = P (4, 4) ways
By the fundamental principle of counting:
The required number of seating arrangements
P(3, 3) x P(4, 4) = 3! x 4! = 6 x 24 = 144
ANSWER:B