List of top Mathematics Questions on permutations and combinations asked in TS EAMCET

The number of 3-digit numbers formed using digits 2,3,5,7,9 without repetition that are divisible by 3 is

There are 7 men and 5 women in a park. The number of ways of arranging them around a circular path such that 4 particular persons which include 2 particular men and 2 particular women never stand together is:

The number of integral solutions of \[ x+y+z=13 \] such that \[ 1\le x\le9,\qquad 0\le y\le9,\qquad 0\le z\le9 \] is

If \(\dfrac{{}^{\,n-1}C_{r-1}}{{}^{\,n}C_r}=\dfrac{3}{5}\) and \(\dfrac{{}^{\,n+1}C_{r+1}}{{}^{\,n}C_r}=\dfrac{11}{7}\), then \({}^{\,n}C_{r+3}\div{}^{\,r}C_{n/2}\) is equal to:

Number of 5-digit numbers using digits 3–9 with repetition, divisible by 7.

Committee of 5 from 5 Indians, 4 Americans, 3 Australians with at least one from each and max 2 per country.

Compute $p$ and $q$ ratio for circular + linear arrangements with constraints.

\( T_m \) denotes the number of triangles that can be formed with the vertices of a regular polygon of \( m \) sides. If \( T_{m+1} - T_m = 15 \), then \( m = \)

The number of positive integral solutions of $xyz = 60$ is

The number of ways in which 6 boys and 4 girls can be arranged in a row such that between any two girls there must be exactly 2 boys is

The number of all possible three letter words that can be formed by choosing three letters from the letters of the word FEBRUARY so that a vowel always occupies the middle place is

If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together is

The number of positive integral solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{2025}$ is

All the letters of the word MOTHER are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word MOTHER is

When \( |x|>3 \), the coefficient of \( \frac{1}{x^n} \) in the expansion of \( x^{3/2} (3+x)^{1/2} \) is

The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is

If all the letters of the word MOST are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order then the rank of the word STOM when counted from the rank of the word MOST, is

The number of integers lying between 1000 and 10000 such that the sum of all the digits in each of those numbers becomes 30 is

The number of non negative integral solutions of the equation \( x+y+z+t=10 \) when \( x \ge 2, z \ge 5 \) is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

Number of all possible ways of distributing eight identical apples among three persons is