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Q.

If the number words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k, then k is equal to

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a

1890

b

2835

c

945

d

5670

answer is A.

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Detailed Solution

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MATHEMATICS
${\frac{9!}{2! 2! 2!}}^{10} C_{2} \cdot 2! \Rightarrow \frac{9 \cdot 8 \cdot 7 \cdot 6!}{8} 10 \cdot 9 \Rightarrow 5670 (6!)$

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