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

Question

The number of ways of arranging the letters AAAAA, BBB, CCC, D, EE and F in a row if the letters C are separated from one another is (A)  13 C 3 (12 !/5 ! 3 ! 2 !) (B) (13 !/5 ! 33 ! 2 !) (C) (14 !/3 ! 3 ! 2 !) (D) (15 !/5 !(3 !)2 2 !)-(13 !/5 ! 3 ! 2 !)-(12 !/5 ! 3 !) 13 C 2

Tardigrade Admin · Accepted Answer

Correct answer is (a) 13 C 3 (12 !/5 ! 3 ! 2 !)Correct answer is (d) (15 !/5 !(3 !)2 2 !)-(13 !/5 ! 3 ! 2 !)-(12 !/5 ! 3 !) 13 C 2

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

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

$\frac{13 !}{5 ! 33 ! 2 !}$

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

$\frac{15 !}{5 ! ( 3 ! ) ^{2} 2 !} - \frac{13 !}{5 ! 3 ! 2 !} - \frac{12 !}{5 ! 3 !}^{13} C_{2}$

Correct answer is (a) $^{13} C_{3} \frac{12 !}{5 ! 3 ! 2 !}$ Correct answer is (d) $\frac{15 !}{5 ! ( 3 ! ) ^{2} 2 !} - \frac{13 !}{5 ! 3 ! 2 !} - \frac{12 !}{5 ! 3 !}^{13} C_{2}$

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

13C3​5!3!2!12!​

5!33!2!13!​

3!3!2!14!​

5!(3!)22!15!​−5!3!2!13!​−5!3!12!​13C2​