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

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

Tardigrade Admin · Accepted Answer

(A) 7 C 2 × (6 !/2 ! ⋅ 2 !)=21 × 180=3780. (B) 7 C 2 × (6 !/2 ! ⋅ 2 !)- 6 C 2 × (5 !/2 !)=3780-900=2880. (C) 6 C 2 × (5 !/2 !)=900 (D) (6 !/2 !)=360 .

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

2C's are separated is 3780.

2C's and 2L's are separated is 2880.

2C's are separated but 2L's are together is 900.

2C's and 2L's are together is 360

(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) $\frac{6 !}{2 !} = 360.$

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

2C's are separated is 3780.

2C's and 2L's are separated is 2880.

2C's are separated but 2L's are together is 900.

2C's and 2L's are together is 360

(A) 7C2​×2!⋅2!6!​=21×180=3780. (B) 7C2​×2!⋅2!6!​−6C2​×2!5!​=3780−900=2880. (C) 6C2​×2!5!​=900 (D) 2!6!​=360.

(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) $\frac{6 !}{2 !} = 360.$