Permutation and combination practice · Mixed difficulty

Five digit numbers divisible by 9 are to be formed by using the digits $0,1,2,3,4,5,7$ without repetition. The total numbers of such numbers is $\lambda^3$, then $\lambda$ is

$\sum\limits_{0 \leqslant i} {\sum\limits_{ < j < } {\sum\limits_{k < l} {\sum\limits_{ \leqslant n} {} } } }$ is equal to

How many ways are three to arrange the letters in the word ‘GARDEN’ with the vowels in alphabetical order?

If the letters of the word SACHIN arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at series number

How many different non-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places?

The units digit of ${17^{2009}} + {11^{2009}} - {7^{2009}}$ is

The value of $\sum\limits_{{r=0}}^{n-1}{ }^n C_r /\left({ }^n C_r+{ }^n C_{r+1}\right)$ equals

Let $S=\left\{\left[\begin{array}{cc}18 & a \\ b & 25\end{array}\right]: a, b \in {N}\right\}$ The number of singular matrices in $S$ is

Number of words of 4 letters that can be formed with the letters of the word IIT JEE, is

Let $A=\{x \mid x$ is a prime number and $x < 30\}$. The number of dif- ferent rational numbers whose numerator and denominator belong to $A$ is

The total number of $n$-digit numbers $(n > 1)$ having the property that no two consecutive digits are same, is

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

The sum of all 3- digited numbers that are divisible by either 3 or 4 but not by 48 is

Number of ordered triplets $(x, y, z)$ such that $x, y, z$ are primes and $x^y+1=z$, is

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two $S$ are adjacent?

The figure 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is

The total number of seven-digit numbers the sum of whose digits is even is

Find the remainder when $1 !+2 !+3 !+\ldots+n$! is divided by 15, if $n \geq 5$.

No.of ways of seating 20 persons at two round tables. Seating 10 to each table is

Number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

The number of words that can be formed out of the letters of the words ‘ARTICE’ so that the vowels occupy even places, is

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

The number less than 1000 that can be formed using the digits $0,1,2,3,4,5$ when repetition is not allowed is equal to

If the letters of the word 'NAAGI' are arranged as in a dictionary then the rank of the given word is

The letters of the word 'HEXAGON' are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangements is

The number of arrangements which can be made using all the letters of the word LAUGH, if the vowels are adjacent, is

The number of ways in which the letters of 'ARRANGE' be arranged so that "Two R's come together but Two A's do not come together is

The total number of three-digit numbers, the sum of whose digits is even, is equal to

In a 12 - storey house ten people enter a lift cabin. It is known that they will left in groups of 2,3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop to the second storey is