R D Sharma Solutions for Chapter: Combinations, Exercise 3: EXERCISE 17.3

How many words each of $3$ vowels and $2$ consonants canbe formed from the letters of the word $\mathrm{INVOLUTE}$?

Find the value of $k$ if the number of permutations of $n$ different things taken $r$ at a time such that two specified things occur together is ${\hspace{0.17em}}^{n-k}{C}_{r-k}(r-1)!·k!$

Find the number of ways in which:
a selection, of four letters can be made from the letters of the word $"\mathrm{PROPORTION}"$.

Find the number of ways in which:
an arrangement, of four letters can be made from the letters of the word $"\mathrm{PROPORTION}"$.

How many words can be formed by taking $4$ letters at a time from the letters of the word $\text{'}\mathrm{MORADABAD}\text{'}$?

A business man hosts a dinner to $21$ guests. He is having $2$ round tables which can accommodate $15$ and $6$ persons each. In how many ways can he arrange the guests?

How many words can be formed of $4$ letters taken from the word $\text{'}\mathrm{EXAMINATION}\text{'}$.

A tea party is arranged for $16$ persons along two sides of a long table with $8$ chairs on each side. Four persons wish to sit on one particular side and two on the other side. Number of ways in which persons can be seated are ${}^{n}C_4\times {\left(a!\right)}^2$. Find the value of $\left(n+a\right)$.