Question

Number of ways in which 6 different toys can be distributed equally among 3 children is also equal to

• A. number of ways in which all the letters of the word KUMKUM can be arranged in a definite order.
• B. number of different signals which can be obtained from 10 different flags taken two at a time keeping one above the other.
• C. number of ways in which five different marbles can be placed in three different boxes so that no box remains empty.
• D. number of ways in which all the letters of the word CALCULUS can be arranged without changing the order and position of non alike letters

Answer 1

Answer: (A), (B), (D)

Answer is $\left(\frac{6!}{2!2!2!3!}\right)\times 3!=\frac{6!}{2!2!2!}=90$
(A) $\frac{6!}{2!2!2!}\Rightarrow$ (A) is correct.
(B) ${}^{10}{C}_2\cdot 2!\Rightarrow$
(B) is correct.

(Using Division and Distribution)
(D) A and $S$ remains in $2^{\text{nd }}$ and $8^{\text{th }}$ position
Hence, number of ways $=\frac{6!}{2!2!2!}\Rightarrow$(D) is correct.