The number of ways of arranging the letters AAAAA, BBB, CCC, D, EE and F in a row, if the letters B are separated from one another, is equal to

Question

The number of ways of arranging the letters AAAAA, BBB, CCC, D, EE and F in a row, if the letters B are separated from one another, is equal to (A) (13 !/5 ! 3 ! 3 ! 2 !) (B) (14 !/3 ! 3 ! 2 !) (C) (15 !/(3 !)2 2 ! 5 !) (D) 13C3× (12 !/5 ! 3 ! 2 !)

Tardigrade Admin · Accepted Answer

All AAAAA, CCC, D, EE, F can be arranged in (12 !/5 ! 3 ! 2 !) ways. Between the gaps B can be arranged in 13C3 ways Hence, the total number of ways =13C3× (12 !/5 ! 3 ! 2 !)

Q. The number of ways of arranging the letters $AAAAA, BBB, CCC, D, EE$ and $F$ in a row, if the letters $B$ are separated from one another, is equal to

$\frac{13 !}{5 ! 3 ! 3 ! 2 !}$

$\frac{14 !}{3 ! 3 ! 2 !}$

$\frac{15 !}{( 3 ! ) ^{2} 2 ! 5 !}$

$^{13} C_{3} \times \frac{12 !}{5 ! 3 ! 2 !}$

All $AAAAA, CCC, D, EE, F$ can be arranged in $\frac{12 !}{5 ! 3 ! 2 !}$ ways.
Between the gaps $B$ can be arranged in $^{13} C_{3}$ ways
Hence, the total number of ways $=^{13} C_{3} \times \frac{12 !}{5 ! 3 ! 2 !}$

Q. The number of ways of arranging the letters AAAAA,BBB,CCC,D,EE and F in a row, if the letters B are separated from one another, is equal to

5!3!3!2!13!​

3!3!2!14!​

(3!)22!5!15!​

13C3​×5!3!2!12!​