Permutation and combination practice · Medium

Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated, is

In a shooting competition, a man can score 5, 4, 3, 2 or 0 points for each shot. Then, the number of different ways in which he can score 30 in seven shots, is

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:

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

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

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

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

The number of numbers between 2,000 and 5,000 that can be formed with the digits $0,1,2,3,4$, (repetition of digits is not allowed) and are multiple of 3 is?

The letters of the word 'VICTORY' are arranged in all possible ways, and the words thus obtained are arranged as in a dictionary. Then the rank of given word is

If the words formed by using the letters of the word 'AGAIN' are arranged in the form of dictionary, then $50^{\text {th }}$ word is

From 5 consonants, 4 vowels and 3 capital letters, the number of words beginning with a capital letter and containing 3 consonants and 2 vowels that can be made is

In how many ways can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student?

The number of rational numbers lying in the interval $(2002,2003)$ all whose digits after the decimal points are non-zero and are in decreasing order, is

Two straight lines intersect at a point $O$. Points $A_1, A_2, \ldots, A_n$ are taken on one line and points $B_1, B_2, \ldots, B_n$ on the other. If the point $O$ is not to be used, then the number of triangles that can be drawn using these points as vertices, is

The number of ways of selecting 4 letters from the word EXAMINATION, is

There are 5 boys and 3 girls. In how many ways can they be seated in a row, so that all the three girls do not sit together?

The total number of six-digit numbers that can be formed, having the property that every succeeding digit is greater than the preceding digit, is

Value of $\frac{n !}{(n-r) !}$ when $n=6, r=2$ is $5{m}$. The value of $m$ is

The number of ways in which the letters of the word ARRANGE be arranged so that "two A's are together but not two R's

The number of ways of arranging six persons (having $A, B, C$ and $D$ among them) in a row so that $A, B, C$ and $D$ are always in order $A B C D$ (not necessarily together) is

If $\frac{2}{9 !}+\frac{2}{3 ! 7 !}+\frac{1}{5 ! 5 !}=\frac{2^a}{b !}$, where $a, b \in N$, then the ordered pair $(a, b)$ is

The number of ways in which a score of 11 can be made from a through by three persons, each throwing a single die once, is

The number of proper divisors of 1260 , is

$\sum\limits_{0 \leqslant i} {\sum\limits_{ \leqslant j \leqslant 10} {^{10}{C_j}^j{C_i}} }$ is equal to

The total number of 3 digit even numbers that can be composed from the digitis $1,2,3, \ldots$. , 9 when the repetition of digits is not allowed, is

Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5\}$. If $f: A \rightarrow B$ is an one-one function and $f(x)=x$ holds only for one value of $x \in\{1,2,3,4,5\}$, then the number of such possible function is

If number of numbers greater than 3000 , which can be formed by using the digits $0,1,2,3,4,5$ without repetition, is $n$ then $\frac{n}{230}$ is equal to

The number of words which can be formed out of letters $a, b, c, d, e, f$ taken 3 together, each containing one vowel at least is

Ajay writes letters to his five friends and addresses the corresponding. The number of ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes is