Suppose four balls labelled $1, 2, 3, 4$ are randomly placed in boxes $B_1, B_2, B_3, B_4$. The probability that exactly one box is empty is

In a group of $6$ boys and $4$ girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

The total number of ways in which a student can select a book is $63.$ If he is allowed to select at most $n$ books from a collection of $2n+1$ books, then $n=$?

A question paper is divided into two parts $A$ and $B$ and each part contain 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is

The total number of ways in which a student can select a book is $63.$ If he is allowed to select at most $n$ books from a collection of $2n+1$ books, then $n=$?

Six people of different heights are getting in line to buy dosa. Let the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of height, from front to back be $N.$ Find the remainder when $N$ is divided by $10.$

How many different words can be made out of the letters of INVOLUTE so that each word may contain $3$ vowels and $2$ consonants?

How many different algebraic expressions can be made by combining the letters $a,b,c,d$ and $e$ in this order with the signs $\text{'}+\text{'}$ and $\text{'}-\text{'}$ all the letters taken together?

How many of these words will not contain the two L's together?

In how many ways  can the letter of the word INDEPENDENCE be arranged so that

the words begin with I and end with P?

In how many ways  can the letter of the word INDEPENDENCE be arranged so that

the vowels never occur together ?

In how many ways can the letter of the word INDEPENDENCE be arranged so that the words begin with P?

In how many ways can the letters of the word ARRANGE he arranged so that

neither two A's nor two R's; are together 

The 'cylinder' of a 'Letter-lock' contains $5$ rings. On each ring 6 different letters are engraved. How many unsuccessful attempts may be made to open the lock by a person who does not know the 'key-word'?

How many numbers of five digits can be made with the digits 1,2,3 each of which can be used at most thrice in a number?

There are unlimited number of identical balls of four different colours. How many arrangements of at most $8$ balls in a row can be made by using them?

Puneet writes letters to his five friends and address the corresponding envelopes. If $\lambda$ be the numbers of total ways in which the letters can be placed in the envelopes so that at least three of them are in the wrong envelopes, then the value of $\lambda -100$ is 

For any two events $A, B$ if $P(A\cup B)=aP(A\cap B)+bP\left(A\right)+cP\left(B\right),$ then $3a+2b+5c=?$

Find the number of ways of selecting a team of $10$ players out of $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded.

Let the number of combinations of seven digit numbers with distinct digits of the form $a_1{a}_2{a}_3{a}_4{a}_5{a}_6{a}_7$ $\left(a_i\ne 0\forall i=1,2,\dots ,9\right)$ be present in decimal system, such that $a_1<a_2<a_3<a_4>a_5>a_6>a_7$ is equal to $k$, then $\frac{\mathrm{k}}{50}$ is equal to :