Permutation and combination practice · Easy

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is

The sum of all 4 digited numbers that can be formed using the digits $1,2,4,5,6$ without repetition is

If ${\;^{12}}{P_r} = {\;^{11}}{P_6} + 6.{\;^{11}}{P_5}$ then $r$ is equal to

The number of lines drawn through 6 points lying on a circle is

How many 10 digits numbers can be written by using digits 9 and 2?

Total number of three letter words that can be formed from the letters of the word 'SAHARANPUR' is equal to

In a circus there are ten cages for accommodating ten animals. Out of these four cages are so small that five out of 10 animals cannot enter into them. In how many ways will it be possible to accommodate ten animals in these ten cages?

If the permutations of $a,b,c,d,e$ taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation $debac$ is

Let $p$ be a prime number such that $p \geq 3$. Let $n=p !+1.$ The number of primes in the list $n + 1, n + 2, n + 3, ...., n + p − 1$ is

How many numbers divisible by 5 and lying between 3000 and 4000 that can be formed from the digits 1, 2, 3, 4, 5, 6 (repetition of digits is not allowed)?

If $[y]$ denote the greatest integer $\leq y$, and $2\left[\frac{x}{8}\right]^2+3\left[\frac{x}{8}\right]=20$, then $x$ lies in the smallest interval $[a, b)$ where $b-a$ is equal to

How many different arrangements can be made out of the letters in the expansion $A^2 B^3 C^4$, when written in full?

If ${\;^n}{P_r} = 30240$ and ${\;^n}{C_r} = 252$, then the ordered pair $\left( {n,\;r} \right)$ is equal to

In an examination a minimum is to be secured in each of 5 subjects for a pass. The number of ways in which a student can fail is

$A_1, A_2 \ldots A_n$ are points on the line $y=x$ lying in the positive quadrant such that $O A_n=n O A_{n-1}, O$ being the origin. If $O A_1=1$ and the coordinates of $A_n$ are $(2520 \sqrt{2}, 2520 \sqrt{2})$, then $n=$

Let ${P_m}$ stand for ${\;^m}{P_m}.$ Then, $1 + {P_1} + 2\;{P_2} + 3\;{P_3} + \ldots + n.{P_n}$ is equal to

The number of ways in which the letters of the word "STRANGE" can be arranged so that the vowels may appear in the odd places, is

The number of all possible words that can be formed using the letters of the word “MATHEMATICS” is

Find the number of ways of arranging the letters of the word 'BANANA'

The number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour, is

Let $A$ be a set of $n(\geq 3)$ distinct elements. The number of triplets $(x, y, z)$ of the set $A$ in which atleast two coordinates are equal to

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n=10$, the value of $n$ is

A seven-digit number made up of all distinct digits $8,7,6,4,2, x$ and $y$ is divisible by 3. Then, possible number of order pair $(x, y)$ is

If $r,\;s,\;t$ are prime numbers and $p,q$ are the positive integers such that LCM of $p,\;q$ is ${r^2}{s^4}{t^2}$, then the number of ordered pairs $\left( {p,\;q} \right)$ is

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

How many words can be made from the letters of the word ‘COMMITTEE’?

Every one of the 10 available lamps can be switched on to illuminate certain Hall. The total number of ways in which the hall can be illuminated, is

A four digit number of distinct digits is formed by using the digits $2,3,4,5,6,7,8$. The number of such numbers which are divisible by 25, is

The least positive integer $n$ for which ${ }^{n-1} C_5+{ }^{n-1} C_6 < { }^n C_7$ is