Permutation and combination practice · Easy

The number of ways of dividing 10 girls into two groups of 5 each so that two shortest girls are in the different groups is:

There are 5 roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back, is

Suppose $p \in {N}, n={ }^{{P}} C_2$ and $m={ }^{{n}} C_2$. If $4 m: n=$ $18: 1$, then $p$ is equal to

In an examination, there are 11 papers. A candidate has to pass in at least 6 papers to pass the examination. The number of ways in which the candidate can pass the examination is:

All letters of the word AGAIN are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

The remainder when $x = 1! + 2! + 3! + 4!+\ldots+100$ ! is divided by 240, is

Out of 10 red and 9 white balls, 5 red and 4 white balls can be drawn in number of ways $=$

Four dice are rolled. The number of possible outcomes in which at least one dice shows 2 is

$A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ of $A$ is again chosen. The number of ways of choosing $P$ and $Q$, so that $P \cap Q=\phi$, is

On a railway route there are 15 stations. The number of tickets required in order that it may be possible to book a passenger from every station to every other is

If ${ }^{56} P_{r+6}:{ }^{54} P_{r+3}=30800: 1$, then $r$ is equal to

The number of arrangements of the word "IDIOTS" such that vowels are at the places which from three consecutive terms of an A.P. is :

How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?

The number of signals that can be sent using 5 flags of different colours, taking one or more at a time, is

The number of ways can 10 letters be placed in 10 marked envelopes, so that no letter is in the right envelope are

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is $E$, then the total number of all such words is :

An urn contains 3 red pens, 4 green pens and 6 yellow pens. The number of ways of drawing 4 pens from the urn, if atleast one red pen is to be included in the draw, is (all the pens are different from each other)

The number of functions $f$ from the set $A=\{0,1,2\}$ into the set $B=\{0,1,2,3,4,5,6,7\}$ such that $f(i) \leq f(j)$ for $i < j$ and $i, j \in A$, is

How many words can be made from the letters of the word DELHI, if $L$ comes in the middle of every word?

Let $\mathrm{T}_4$ denotes the number of triangles which can be formed by using the vertices of a regular polygon of $n$ sides, If $T_{n+1}-T_n=21$, then $n$ equals.

The number of diagonals that can be drawn by joining the vertices of an octagon is

Find the number of chains that can be prepared using 5 different colored beads

There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is

$n$ lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut, is

5 different objects are to be distributed among 3 persons such that no two persons get the same number of objects. Number of ways this can be done, is

The number of ways by which letter of word ASSASSINATION can be arranged such that all vowels come together is:

A telegraph has 5 arms and each arm is capable of 4 distinct positions, including the position of rest. The total number of signals that can be made is

If all the words (with or without meaning having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

The total number of words that can be formed using all letters of the word 'RITESH' that neither begins with I nor ends with $\mathrm{R}$, is

The number of ways in which 10 boys and 10 girls can be seated in a row so that boys and girls alternate is