In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
A. 144
B. 288
C. 12
D. 256
Answer: Option A
Solution(By Examveda Team)
Let the Arrangement be,B G B G B G B
4 boys can be seated in 4! Ways
Girl can be seated in 3! Ways
Required number of ways,
= 4! × 3!
= 144
Join The Discussion
Comments ( 3 )
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
when seating 4 boys and 3 girls alternatively in a row, consider them as distinct entities. you have 7 individuals to arrange.
the possible arrangements for B (boys) and G (girls) are as follows:
1. BGBGBGB
2. GBGBGBB
3. GBGBBGB
there are 2 possible arrangement for the sequence of B and G. within each gender, the individuals can be arranged among themselves.
so, the total number of ways is (2times 4!time 3!=2times 24 times 6 = 288).
therefore, there are 288 ways to seat 4 boys and 3 girls alternatively in a row.
Dear Nagamani,
! means "Factorial"
Ex: 1!=1
2!=1x2=2
3!=1x2x3=6
4!=1x2x3x4=24
......................
......................
n!=1x2x3x4x5x6x........xn
Thanks..
i dont understand these solutions what 4!3!means what '!' symbolises