Question

The letters of the word "CALCULUS" are arranged in all possible ways. Then the number of words in which

• A. 2C's are separated is 3780.
• B. 2C's and 2L's are separated is 2880.
• C. 2C's are separated but 2L's are together is 900.
• D. 2C's and 2L's are together is 360

Answer 1

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

(A) ${ }^7 C _2 \times \frac{6 !}{2 ! \cdot 2 !}=21 \times 180=3780$.
(B) ${ }^7 C _2 \times \frac{6 !}{2 ! \cdot 2 !}-{ }^6 C _2 \times \frac{5 !}{2 !}=3780-900=2880$.
(C) ${ }^6 C _2 \times \frac{5 !}{2 !}=900$
(D) $\frac{6 !}{2 !}=360 . $