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

The number of 3-digit even numbers that can be formed with the digits 0, 1, 2, 3, 4, 5, 6 are
The sum of all 3-digit numbers that can be formed using $1,2,3,4$ without repetitions is
If ${}^9P_5 = (504)({}^6P_r)$, then the value of $r$ is equal to:
The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is
Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:
Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is
Four fair dice are rolled. Then the number of ways in which the sum of upper faces of four dices can be six, is
${}^{21}C_1 + {}^{21}C_2 + \dots + {}^{21}C_{10} =$
25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects. Then the number of ways of forming such groups, is
Let \( A = \{0,2,4,6,8\} \). The number of 5-digit numbers that can be formed using the digits in \( A \) without replacement, is
If \( ^{11}P_r = 7920 \), then the value of \( r \) is equal to
If \(\sum_{k = 0}^{n + 1} \binom{n+1}{k} = 512\) , then \(\sum_{k = 0}^{n} \binom{n}{k} =\)
\(\frac{8}{4}\left(^{7}P_{4}\right)\) equals
Let S be the set of all 5-digit numbers having only the digits 0 and 1. Then \(n(S) =\)
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