Question

The number of words with or without meaning can be formed from the word MATHEMATICS where C, S does not come together is

• A. $\frac{9}{8}$ x 10!
• B. $\frac{1}{8}$ x 10!
• C. $\frac{5}{8}$ x 10!
• D. $\frac{1}{2}$ x 10!

Answer 1

Answer: (A)

$\frac{9}{8}$ x 10!

Answer 2

We need to find the number of words that can be formed using the letters of the word MATHEMATICS such that the letters C and S do not come together.
First, we can find the total number of ways to arrange the letters of the word MATHEMATICS, which is given by:
n = $\frac{11!}{(2!2!2!)}$ = 4989600
Next, we can find the number of arrangements where the letters C and S come together. We can consider the group CS as a single letter, and then we have 10 letters to arrange. There are $\frac{10!}{(2!2!)}$ ways to arrange these 10 letters, and there are 2 ways to arrange the letters C and S within the group CS. Therefore, the number of arrangements where C and S come together is:
m = $\frac{10!}{(2!2!)}$ x2= 907200
Finally, we can subtract the number of arrangements where C and S come together from the total number of arrangements to get the number of arrangements where C and S do not come together:
n - m = 4989600 - 907200 = 4082400
Therefore, there are 4082400 words that can be formed from the word MATHEMATICS such that the letters C and S do not come together.
Therefore option A i.e; $\frac{9}{8}$ x 10! is correct.
Answer. A