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

Answer 1

Answer: (B), (C), (D)

Actual answer is equal to $\frac{6 !}{2 ! 2 ! 2 !}=90 \quad$
(A)$ 72$ ;
(B) $\frac{6 ! 3 !}{2 ! 2 ! 2 ! 3 !}$;
(C) ${ }^{10} C _2 \cdot 2 !=90$;
(D) ${ }^6 C _4 \cdot 3 !=90$