List of top Mathematics Questions on Combinatorics asked in KEAM

The coefficient of $x^{8}$ in the expansion of $(x^{2}+\sqrt{1-x^{2}})^{5}+(x^{2}-\sqrt{1-x^{2}})^{5}$ is

If $^{n}P_{5}=6720$ and $^{(n-1)}P_{4}=840$, then $^{n}P_{3}$ is equal to

If $^{n}C_{4}=1365$ then the value of n is equal to

A polygon has 170 diagonals. The number of sides of the polygon, is

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 elements is:

A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} \( \alpha - \beta \).