R D Sharma Solutions for Chapter: Permutations, Exercise 5: EXERCISE 16.5

Find the number of numbers, greater than a million, that can be formed with the digits $2, 3, 0, 3, 4, 2, 3$.

There are three copies each of $4$ different books. In how many ways can they be arranged in a shelf?

How many arrangements can be made by using all the letters in the word $\text{'}\mathrm{MATHEMATICS}\text{'}$. How many of the arrangements begin with $\mathrm{C}$? How many of the arrangements begin with $\mathrm{T}$?

A biologist studying the genetic code is interested to know the number of possible arrangements of $12$ molecules in a chain. The chain contains $4$ different molecules represented by the initials $A$ (for Adenine), $C$ (for Cytosine), $G$ (for Guanine) and $T$ (for Thymine) and $3$ molecules of each kind. How many different such arrangements are possible?

In how many ways can $4$ red, $3$ yellow and $2$ green discs be arranged in a row if the discs of the same colour are indistinguishable?

How many numbers greater than $1000000$ can be formed by using the digits $1,2,0,2,4,2,4$?

In how many ways can the letters of the word $\mathrm{ASSASSINATION}$ be arranged so that all the $\mathrm{S}’\mathrm{s}$ are together? (Write only numerical value)

Find the total number of permutations of the letters of the word $\text{'}\mathrm{INSTITUTE}\text{'}$.