R S Aggarwal Solutions for Exercise 5: EXERCISE 8E

Find the total number of permutations of the lettersof the word given below:

Number of words that can be formed with the letters of the word $\text{'}\mathrm{CAPTAIN}\text{'}$ in which $\mathrm{C}$ and $\mathrm{T}$ are never together is $k$. Find the value of $k$.

In how many ways can the letters of the word $\text{'}\mathrm{ASSASSINATION}\text{'}$ be arranged so that all $\mathrm{S}\text{'}\mathrm{s}$ are together?

How many arrangements can be made by using all the letters of the word $\text{'}\mathrm{MATHEMATICS}\text{'}$?

If $k$ words can be made with the word $\mathrm{MATHEMATICS}$ which begin with $\mathrm{C}$, then find the value of $k$

If $k$ words can be made with the word $\mathrm{MATHEMATICS}$ which begin with $\mathrm{T}$, then find the value of $k$

In how many ways can the letters of the word $\text{'}\mathrm{INTERMEDIATE}\text{'}$ be arranged so that:

The vowels always occupy even places?

How many $7$-digit numbers can be formed with the digits $2, 3, 4, 5, 4, 3, 2$ so that the odd digits occupy the odd places?