Fundamental Principle of Counting

Q. The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0,1,2,3,4,5$ (repetition of digits is allowed) is:

1. $288$
2. $306$
3. $310$
4. $360$

Q. The number of onto functions $f$ from $\{1,2,3,....,20\}$ to $\{1,2,3,...,20\}$ such that $f\left(k\right)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is :

1. $5!\times 6!$
2. $5^6\times 15$
3. $6^5\times \left(15\right)!$
4. $\left(15\right)!\times 6!$

Q. Let $S=\{1,2,3,4,5,6,7\}$. Then the number of possible functions $f:S\to S$ such that $f(m\cdot n)=f\left(m\right)\cdot f\left(n\right)$ for every $m,n\in S$ and $m\cdot n\in S$ is equal to

Q.

Along a railway line, there are 20 stations. The number of different tickets required in order so that it may be possible to travel from every station to every station is what ?

Q. How many $2$ digit even numbers can be formed from the digits $1,2,3,4,5$ if the digits can be repeated?

Q.

The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is

1. 12

2. 24

3. 18

4. None of these

Q.

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

Q.

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

Q.

Describe the sample space for the indicated experiment: A coin is tossed three times.

Q. Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{1}{2}$
4. $\frac{2}{7}$

Q.

Form the greatest six-digit odd number and smallest six-digit even number using the digits from $1$ to $9$ only once. What will be the sum of these numbers?

Q. If the number of five digit numbers with distinct digits and $2$ at the $10\text{th}$ place is $336k$, then $k$ is equal to :

1. $7$
2. $4$
3. $6$
4. $8$

Q. The traffic lights at three different road crossings change every $24$ seconds, $36$ seconds, and $72$ seconds respectively. If they all change simultaneously at $8:20:00$ a.m., then they will again change simultaneously at

1. $8:21:12$ a.m.
2. $8:20:12$ a.m.
3. $8:22:00$ a.m.
4. $8:21:12$ p.m.

Q. How many numbers can be made with the digits 3, 4, 5, 6, 7, 8 lying between 3000 and 4000 which are divisible by 5 while repetition of any digit is not allowed in any number

1. 60
2. 12
3. 120
4. 24

Q.

How many three -digit odd numbers are there ?

Q. From the digits 1, 2, 3, 4, 5 and 6 how many 3 digit Even Numbers can be formed when repetition is not allowed

Q.

Verification of a login name and password is known as______

Q.

The number of 5-digit numbers which are divisible by 3 that can be formed by using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9, when repetition of digits is allowed, is

1. 

2. 

3. 

4. 

Q.

Number of all four digit numbers having different formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

1. 24

2. 30

3. 125

4. 100

Q.

How many words of $4$ constant & $3$ vowel can be formed from $6$ constant & $5$ vowels ?

1. $75000$

2. $756000$

3. $75600$

4. $Noneofthese$

Q.

Twelve students compete in a race. In how many ways first three prizes be given?

Q. The total number of $9$ digit numbers which have all different digits is

1. $9!\times 2!$
2. $10!$
3. $9\times 9!$
4. None of the above

Q. the number of positive integers less than 1, 00, 000 which contain exactly one 2, one 5 and one 7 in decimal representation is

Q.

The number of $5$ digit telephone numbers having at least one of their digits repeated is?

1. $90,000$

2. $1,00,000$

3. $30,240$

4. $69,760$

Q.

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of february calendars should it prepare to serve for all the possibilities it future years ?

Q.

Define e-reservation

Q. The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

1. $\frac{1}{36}$
2. $0$
3. $\frac{1}{3}$
4. $\frac{1}{12}$

Q. Find the number of $4$ letter words, with or without meaning, which can be formed out of the letters of the word $\text{ROSE,}$ where the repetition of the letters is not allowed.

Q.

How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?

Q.

The total number of $5$ digit numbers of different digits in which the digit in the middle is the largest, is

1. $32\left(5!\right)$

2. $35\left(3!\right)$

3. $32\left(3!\right)$

4. None of these.