A football stadium has four entrance gates and nine exits. In how many different ways can a man enter and leave the stadium?

There are six doors in a hostel. In how many ways can a student enter the hostel and leave by a different door?

In how many ways can a man send three of his children to seven different colleges of a certain town?

Suppose there are five main roads between the cities A and B. In how many ways can a man go from a city to the other and return by a different road?

There are five main roads between the cities A and B and 4 between B and C. In how many ways can a person drive from A to C and return without driving on the same road twice?

How many numbers of at least three different digits can be formed from the integers $\rm 1, 2, 3, 4, 5, 6$ ?

How many numbers of three digits less than 500 can be formed from the integers  $\rm 1, 2, 3, 4 , 5, 6\; $?

Of the numbers formed by using all the figures$\rm 1, 2, 3, 4, 5 $ only once, how many are even?

How many numbers between 4000 and 5000 can be formed with the digits $\rm 2, 3, 4 ,5, 6, 7$ ?

How many numbers of three digits can be formed from the integers $\rm 2, 3, 4, 5, 6 $ ? How many of them will be divisible by 5 ?

Find the number of permutations of five different objects taken three at a time.

If three persons enter a bus in which there are ten vacant seats, find in how many ways they can sit.

How many plates of vehicles consisting of 4 different digits can be made out of the integers $\rm 4, 5, 6, 7, 8, 9 \;$? How many of these numbers are divisible by 2?

How many numbers of 4 different digits can be formed from the digits $\rm 2, 3, 4, 5, 6, 7 $ ? How many of these numbers are $ i) $ divisible by 5$\;$ $ ii)$  not divisible by 5. 

How many 5-digit odd numbers can be formed using the digits $\rm 3, 4, 5, 6, 7, 8,$ and $\rm 9 $. If $\rm i)$ repetition of digits is not allowed $\;$ $\rm ii)$ repetition of digits is allowed?

In how many ways can four boys and three girls be seated in a row containing seven seats 

1. if they may sit anywhere
2. if the boys and girls must alternate
3. if all three girls are together
4. if girls are to occupy odd seats

In how many ways can eight people be seated in a row of eight seats so that two particular persons are $\rm a)$ always together $\rm b) $ never together? 

Six different books are arranged on a shelf. Find the number of different ways in which the two particular books are $\rm a) $ always together $\rm b)$ not together. 

In how many ways can four red beads, five white beads, and three blue beads be arranged in a row?

In how many ways can the letters of the following words be arranged?

1. ELEMENT
2. NOTATION
3. MATHEMATICS
4. MISSISSIPPI

If an operation can be performed in m different ways, following which another operation can be performed in n possible ways and the operations are independent, then both operations in succession can be performed exactly in

How many different numbers of three distinct digits can be formed with the digits 0, 1, 2, 3, 4 and 5 which are divisible by 5?

Ten students compete in a race. In how many ways can the first three places be taken?

If (n + 2)! = 210(n- 1)!, then the value of n satisfying the condition is

The number of ways that 8 beads of different colors be string as a neckless is

In how many different ways can 9 people and a host be seated in a circular table of a party?

In how many ways 5 boys and 5 girls sit on a circle so that no two boys sit together?

If a polygon has 44 diagonals, then the number of its sides are:

The number of arrangement of r things out of n number of identical things is

The number of ways to fill the r^th position out of n distinct things in a row is

The value of n, when p(n, 6) =3.p(n, 5) is

The letters of the word SERIES are arranged at random. How many of these arrangements has E's together?

What is the number of permutations of letter of word DAUGHTER. so that vowels occupying even places?

The number of words which can be formed from the letters of the word MAXIMUM, if two consonant cannot occur together is

how many different ways the 7 different colored beads can be strung on a necklace?

If p(n, r) = C(n, r), then