Permutation and combination practice · Easy

A meeting is to be addressed by 5 speakers A, B, C, D, E. In how many ways can the speakers be ordered, if $B$ must not precede A (immediately or otherwise)?

If $\frac{1}{6 !}+\frac{1}{7 !}=\frac{x}{8 !}$, then the value of $x=2^m$. The value of $m$ is

There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that two particular ladies refuse to sit beside a particular gentleman?

Let $S_n=\sum\limits_{{r=1}}^n r ! ; (n > 6)$, then $S_n-7\left[\frac{S_n}{7}\right]$ (where, [ ] denotes the greatest integer function) is equal to

The number of positive integers with the property that they can be expressed as the sum of the cubes of 2 positive integers in two different ways is

The value of ${\;^n}{P_r}$ is equal to

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

Total number of divisors of $n=3^5 \cdot 5^7 \cdot 7^9$ that are of the form $4 \lambda+1, \lambda \geq 0$, is equal to

Among $9!$ permutations of the digits $1,2,3, \ldots, 9$. Consider those arrangements which have the property that if we take any five consecutive positions, the product of the digits in those positions is divisible by 7, the number of such arrangements is

Let $A$ denotes the property that two elements of $A=\{1,5,9,13, \ldots, 1093\}$ add upto 1094. Then, maximum number of elements in $A$ can be

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64 . The number of telephone numbers having all six digits distinct is

The number of polynomials of the form $x^3+a x^2+b x+c$ that are divisible by $x^2+1$, where $a$, $b, c \in\{1,2,3,4,5,6,7,8,9,10\}$, is

The number of ways in which 6 different beads can be string into a necklace is

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

The number of ways in which you can put five beads of five different colours to form a necklace is:

Five persons are to address a meeting. If a specified speaker is to speak before another specified speaker, find the number of ways in which this could be arranged. In how many of these arrangements will the first speaker come immediately before the second?

In how many ways a garland can be made from exactly 10 flowers?

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is

The number of ways in which 5 pictures can be hung from 7 picture nails on the wall is

How many nine digit numbers can be formed by using the digits $2,2,3,3,5,5,8,8,8$ so that the odd digits occupy even positions?

Total number of divisors of $n=2^5 \cdot 3^4 \cdot 5^{10} \cdot 7^6$ that are of the form $4 \lambda+2, \lambda \geq 1$, is equal to

The number of 4-digit even numbers that can be formed using $0,1,2,3,4,5,6$ without repetition is

Seven women and seven men are to sit round a circular table such that there is a man on either side of every women; the number of seating arrangements is

In a class of 10 students there are 3 girls students. The number of ways in which they can be arranged in a row, so that no two girls are consecutive is $k(8!),$ then $k$ is equal to

Let $A$ be a set containing $n$ elements. The number of ways of choosing two subsets $P$ and $Q$ of $A$ such that $P \cap Q=\phi$ is

The number of five digits numbers that can be formed without any restriction, is

Seven atheletes are participating in a race. In how many ways can the first three prizes be won?

The number of ways in which the letters of the word ARRANGE be arranged so that "neither two A's nor two R's are together

How many numbers of 6 digits can be formed from the digits of the number 112233?