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 , is equal to
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 , is equal to
5670
1890
595
657
The Correct Option is A
Solution and Explanation
The total number of words can be calculated by subtracting the number of words when C and S are together from the total words.
\[ \text{M2A2T2HEICS} = \text{total words} - \text{when C and S are together} \]
Now, we calculate the total number of words:
\[ \frac{11!}{2!2!2!} - \frac{10!}{2!2!2!} \times 2 \]
This simplifies to:
\[ \frac{10!}{2!2!} \times 9 = \frac{9 \times 10 \times 9 \times 8 \times 7}{8} \]
Finally, the result is:
5670
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.