List of top Mathematics Questions on permutations and combinations asked in KEAM

If 11Pr=7920 and 11Cr = 330, then the value of r is equal to
The number of numbers greater than 6000 that can be formed from the digits 3, 5, 6, 7 and 9 (no digit is repeated in a number) is equal to
The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is
If p and q are positive integers such that \(^{p+q}P_2=42\ and\ ^{p-q}P_2=20\), then the values of p and q respectively
The number of 3-digit numbers that can be formed from the digits 0, 2, 3, 5, 7 is (repetition is allowed)
The value of ${}^{11}C_{0}+{}^{11}C_{1}+{}^{11}C_{2}+{}^{11}C_{3}+{}^{11}C_{4}+{}^{11}C_{5}$ is
If ${}^{n}P_{r}=840$ and ${}^{n}C_{r}=35$, then the value of $r$ is equal to
Five points are marked on a circle. The number of distinct polygons of three or more sides can be drawn using some (or all) of the five points as vertices is
If $^{5}P_r = {}^{6}P_{r-1}$, then the value of $r$ is
The possible number of arrangements starting with K of the word KALINGA is
\( \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed?
If \( ^{56}P_{r+6} : \, ^{54}P_{r+3} = 30800 : 1 \), then \( r \) is equal to
\( \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to
A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed?
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
The number of diagonals of a polygon with 15 sides is
The arithmetic mean of \( ^nC_0, ^nC_1, \ldots, ^nC_n \) is
If \( ^{56}P_{r+6} : \, ^{54}P_{r+3} = 30800 : 1 \), then \( r \) is equal to
\( \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed?
The number of diagonals of a polygon with 15 sides is
The number of words that can be formed by using all the letters of the word PROBLEM only once is: