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

There are two women participants in a badminton tournament. The number of games the men played between themselves exceeds by 12 the number of games they played with women. If each player played one game with each other, then the number of men in the tournament was
If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to
If \(\frac{{}^nP_{r-1}}{a} = \frac{{}^nP_r}{b} = \frac{{}^nP_{r+1}}{c}\), then
The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is
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 \(n(S) =\)
Let \[ g(x) = 4x + 3 \quad {and} \quad f(g(x)) = x^2 + 9. \] Then the value of \( f(7) \) is equal to
Let \( f(x) = \log_e \left( \frac{x^2 + 30}{11x} \right) \), for \( x \in [5,6] \). Then the point \( c \in (5,6) \) at which \( f'(c) = 0 \) is:
Let \( f(x) = ax^3 + bx^2 + cx + d \). If \( f \) has a local maximum value 21 at \( x = -1 \) and a local minimum value 7 at \( x = 1 \), then \( f(0) \) is equal to:
For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is 
Suppose there are 5 alike dogs, 6 alike monkeys and 7 alike horses. The number of ways of selecting one or more animals from these is
The number of ways in which we can distribute n identical balls in k boxes is 
The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is