Permutation: n Different Things Taken All at a Time When All Are Not Different.

Q.

Write the number of arrangements of the letters of the word BANANA in which two N's come together.

Q.

The number of seven digit integers with sum of the digits equal to $10$ and formed by using the digits $1,2$ and $3$ only is :

1. $77$
2. $42$
3. $35$
4. $82$

Q.

How many three-digit numbers are there with no digit repeated ?

Q.

What is the base number for hexadecimal numbers?

Q. The number of permutations that can be formed out of the letters of the word $"SERIES"$ taking three letters together is:

1. $42$
2. $45$
3. $40$
4. $48$

Q. How many numbers lying between $100$ and $1000$ can be formed with the digits $0,1,2,3,4,5,$ if the repetition of the digits is not allowed?

Q. All possible numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is:

1. $160$
2. $162$
3. $175$
4. $180$

Q. Find the sum of the sequence $7,77,777,7777,...$ to $n$ terms.

Q.

Emily is thinking of a number, which she calls $n$. She finds $\frac{1}{4}$ of the number and then subtracts $3$. Write an expression to represent Emilys number.

Q.

The number of six-digit numbers that can be formed from the digits $1,2,3,4,5,6,7$ so that digits do not repeat and the terminal digits are even is

Q.

The number of ways in which the letters of the word $\text{"ARRANGE"}$ can be arranged such that both $\text{R}$ do not come together is?

1. $360$

2. $900$

3. $1260$

4. $1620$

Q. The product of two , 2 digit number is 2117. The product of their units digits is 27 and that of tens digit is 14. Find the numbers

Q.

How many five-digit number licence plates can be made if
(i) first digit cannot be zero and the repetition of digits is not allowed.
(ii) the first-digit cannot be zero, but the repetition of digits is not allowed?

Q. The total number of numbers greater than $4,00,000$ that can be formed by using the digits $0,2,2,4,4,5$ is

Q.

How many numbers lying between $99\&1000$ be made from the digits $2,3,7,0,8,6$ when the digits occur only once in each number?

Q.

Let n = 1! + 4! + 7! +......+ 400! then tens digit of n is

Q. The number of $7$-digit numbers formed by the digits $1,$ $2$ and $3$ only whose sum of the digits equals $10,$ is

1. $42$
2. $55$
3. $77$
4. $35$

Q. If a $5$ digit number is created using the digits $1,2,3,3,5$. If all possible numbers are arranged in ascending order, then the number situated at ${51}^{th}$ position is

1. $52133$
2. $51323$
3. $51233$
4. $51332$

Q.

$9$ balls are to be placed in $9$ boxes and $5$ of the balls cannot fit into $3$ small boxes. The number of ways of arranging one ball in each of the boxes is

1. $18720$

2. $182730$

3. $17280$

4. $12780$

Q. 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?

Q.

Which letter comes $\frac{2}{5}$ of the way among A and J?

Q.

In the question below is given a group of letters followed by four combinations of digits/symbols numbered

Letter

$\mathrm{W}$

$\mathrm{R}$

$\mathrm{A}$

$\mathrm{P}$

$\mathrm{G}$

$\mathrm{B}$

$\mathrm{M}$

$\mathrm{U}$

$\mathrm{S}$

$\mathrm{E}$

$\mathrm{F}$

$\mathrm{T}$

$\mathrm{N}$

$\mathrm{D}$

Digit / Symbol code

$\$$

$8$

$!$

$2$

$7$

$\#$

$9$

$@$

$?$

$5$

$\mathrm{\beta }$

$4$

$*$

$6$

Conditions :

1. If the middle letter is a vowel, the codes for the first and fourth letter are to be interchanged.
2. If the first two letters are consonants, the first letter is to be coded, no code may be given to the second letter and the remaining three letters are to be coded.
3. If the first letter is a vowel and the last letter is a consonant both are to be coded as the for the Consonant.

What is the code of UGREN ?

1. $*758@$

2. $*785*$

3. $@785@$

4. $@85*$

5. none of these

Q.

Find the total number of permutations of the letters of the word 'INSTITUTE'.

Q.

The smallest odd number formed by using the digits$1,0,3,4\mathrm{and}5$ is

Q.

If in a certain code language $ABCD$ is written as $ZYXW$, then how is the word$DANCE$ written in that code?

Q. All the rearrangements for the letters of the word ${}^{\prime }DEMAN{D}^{\prime }$ are written without including any word that has two $D^{\prime }$s appearing together. If all these are arranged in dictionary order, then the rank of the word $"DEMAND"$ will be

1. $86$
2. $36$
3. $74$
4. $42$

Q. The missing term in the third figure is

1. $6$
2. $8$
3. $1$
4. $0$

Q.

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

Q. The total number of nine-digit numbers that can be formed using the digits $2,2,3,3,5,5,8,8$ and $8$ so that the odd digit occupy the even places is

Q. Find the different permutation of the letters of the word BANANA.