Permutation and Combination_

A letter is taken at random from the letters of the word STATISTICS and another letter is taken at random from the letters of the word ASSISTANT. The probability that they are the same letter is

An eight digit number divisible by $9$ is to be formed by using $8$ digits out of the digits $0,1,\ldots,9$ without replacement. The number of ways in which this can be done is

There are 10 points, out of which 6 are collinear. Number of triangles formed:

How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$, if a path proceeds one step at a time either right (R) or upward (U)?

How many arrangements of the word “DETAIL” place vowels only in odd positions?

The number of ways of forming different $9$-digit numbers from $223355588$ by rearranging digits so that odd digits occupy even positions is

The number of ways to arrange the letters of the English alphabet, so that there are exactly 5 letters between a and b, is:

The number of ways in which 5 days can be chosen in each of the 12 months of a non-leap year, is:

The number of bit strings of length 8, that start with the bit 0 or end with the bits 11 is

The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in arithmetic progression is

The number of bit strings of length 10 that contain either five consecutive 0’s or five consecutive 1’s is

If $42 (^nP_2)=(^nP_4)$ then the value of n is

There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :

If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is  minimum

A polygon has 44 diagonals, the number of sides are

If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is

The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is

The number of words that can be formed by using the letters of the word 'MATHEMATICS' that start as well as end with T is

The sum $^{20}C_8 + ^{20}C_9 + ^{21}C_{10} + ^{22}C_{11} - ^{23}C_{11}$

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen

Lines $L_1, L_2, .., L_10 $are distinct among which the lines $L_2, L_4, L_6, L_8, L_{10}$ are parallel to each other and the lines $L_1, L_3, L_5, L_7, L_9$ pass through a given point C. The number of point of intersection of pairs of lines from the complete set $L_1, L_2, L_3, ..., L_{10}$ is

The value of $\sum ^n_{r=1}\frac{{{{}^nP}}_r}{r!}$ is:

The number of one - one functions f: {1,2,3} → {a,b,c,d,e} is

The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?

Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is