JEE Mains · Maths · STD 11 - 6. permutation and combination
If the number of 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 \(............\).
- A \(1890\)
- B \(945\)
- C \(2835\)
- D \(5670\)
Answer & Solution
Correct Answer
(D) \(5670\)
Step-by-step Solution
Detailed explanation
\(M _2 A _2 T _2 HEICS\) \(=\text { total words }- \text { when } C S \text { are together }\) \(\frac{\lfloor 11}{\lfloor 2\lfloor 2\lfloor 2}-\frac{\lfloor 10}{\lfloor 2\lfloor 2\lfloor 2} \times\lfloor 2\) \(\frac{10}{\lfloor 2\lfloor 2\lfloor 2} \times 9\)…
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