Permutation and combination practice · Mixed difficulty

If there are $n$ number of seats and m number of people have to be seated, then how many ways are possible to do this $(m < n)$ ?

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

How many numbers between 400 and 1000 can be made with the digits 2, 3, 4, 5, 6 and 0?

Three alike red roses and three alike pink roses are used to form a garland. The number of ways is

How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice?

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is

The number of straight lines that can be drawn out of 10 points of which 7 are collinear

A letter lock consists of three rings each marked with 10 different letters. No. of ways to make an unsuccessful attempts to open the lock is

A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

There are $n$ number of sets and m number of people have to be seated, then how many ways are possible to do this $\left( {m < n} \right)?$

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

There are $p$ letters $a, q$ letters $b, r$ letters $c$. The number of ways of selecting $k$ letters out of these if $p < k < q < r$ 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 :

If $S=(1)(1 !)+(2)(2 !)+(3)(3 !)+\ldots+n(n !)$, then

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?

A three digit number $n$ is such that the last two digits of it are equal and differ from the first. The number of such $n'$ is

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

Total number of positive integral solutions of $x_1+x_3+2 x_3=15$ is equal to

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 :