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

The number of diagonals in a hexagon is:

The number of \( 3 \times 3 \) matrices with entries \( -1 \) or \( +1 \) is:

If $\sum_{k=0}^{18} \frac{k}{\binom{18}{k}} = a \sum_{k=0}^{18} \frac{1}{\binom{18}{k}}$, then the value of $a$ is equal to:

If \( ^nP_4 = 5(^nP_3) \), then the value of \( n \) is equal to:

If \( m_1 \) and \( m_2 \) satisfy the relation \( {}^{m+5}P_{m+1} = \frac{11}{2}(m-1)({}^{m+3}P_m) \), then \( m_1 + m_2 \) is

The value of \( x \) satisfying the relation \( 11\binom{x}{3} = 24\binom{x+1}{2} \) is

How many numbers with no more than three digits can be formed using only the digits $1$ through $7$ with no digit used more than once in a given number?

If $^{n}C_{r-1}=28$, $^{n}C_{r}=56$ and $^{n}C_{r+1}=70$, then the value of $r$ is equal to

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?