Number of ways in which the letters A A B B C C can be arranged is also equal to

Question

Number of ways in which the letters A A B B C C can be arranged is also equal to (A) the number of ways in which 4 girls and 4 boys can sit around in circular table if the boys and girls are alternate and a particular boy and a girl are never together in any arrangement. (B) the number of ways in which 6 different toys can be distrubuted equally between Amar, Akbar and Anthony (C) number of ways in which 2 different marbles can be distributed in 10 children if each child gets atmost one marble. (D) the number of ways in which 4 beads can be selected from 6 different beads and put into a circular ring, distinguishing between clockwise and anticlockwise arrangement

Tardigrade Admin · Accepted Answer

Actual answer is equal to (6 !/2 ! 2 ! 2 !)=90 (A) 72 ; (B) (6 ! 3 !/2 ! 2 ! 2 ! 3 !); (C) 10 C 2 ⋅ 2 !=90; (D) 6 C 4 ⋅ 3 !=90

Q. Number of ways in which the letters A A B B C C can be arranged is also equal to

the number of ways in which 4 girls and 4 boys can sit around in circular table if the boys and girls are alternate and a particular boy and a girl are never together in any arrangement.

the number of ways in which 6 different toys can be distrubuted equally between Amar, Akbar and Anthony

number of ways in which 2 different marbles can be distributed in 10 children if each child gets atmost one marble.

the number of ways in which 4 beads can be selected from 6 different beads and put into a circular ring, distinguishing between clockwise and anticlockwise arrangement

Actual answer is equal to $\frac{6 !}{2 ! 2 ! 2 !} = 90$
(A) $72$ ;
(B) $\frac{6 ! 3 !}{2 ! 2 ! 2 ! 3 !}$ ;
(C) $^{10} C_{2} \cdot 2! = 90$ ;
(D) $^{6} C_{4} \cdot 3! = 90$

Q. Number of ways in which the letters A A B B C C can be arranged is also equal to

the number of ways in which 4 girls and 4 boys can sit around in circular table if the boys and girls are alternate and a particular boy and a girl are never together in any arrangement.

the number of ways in which 6 different toys can be distrubuted equally between Amar, Akbar and Anthony

number of ways in which 2 different marbles can be distributed in 10 children if each child gets atmost one marble.

the number of ways in which 4 beads can be selected from 6 different beads and put into a circular ring, distinguishing between clockwise and anticlockwise arrangement

Actual answer is equal to 2!2!2!6!​=90 (A)72 ; (B) 2!2!2!3!6!3!​; (C) 10C2​⋅2!=90; (D) 6C4​⋅3!=90

Actual answer is equal to $\frac{6 !}{2 ! 2 ! 2 !} = 90$
(A) $72$ ;
(B) $\frac{6 ! 3 !}{2 ! 2 ! 2 ! 3 !}$ ;
(C) $^{10} C_{2} \cdot 2! = 90$ ;
(D) $^{6} C_{4} \cdot 3! = 90$