Permutations an...

A committee of $$4$$ persons is to be formed from $$2$$ ladies, $$2$$ old men and $$4$$ young men such that it includes at least $$1$$ lady. at least $$1$$ old man and at most $$2$$ young men. Then the total number of ways in which this committee can be formed is :

The number of values of 'r' satisfying the equation, $${^{39}C_{3r-1}}-{^{39}C_{r^2}}={^{39}C_{r^2-1}}-{^{39}C_{3r}}$$ is?

The number lock of a suitcase has four wheels, each labelled with 10-digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase 

The number of different seven digit numbers that can be written using only three digits 1, 2 & 3 under the condition that the digit 2 occurs exactly twice in each number is-

If $$^{8}C_{r}=^{8}C_{3}$$, then $$r$$ is equal to 

Find $$x$$, if $$\dfrac {1}{4!}-\dfrac {1}{x}=\dfrac {1}{5!}$$.

If $$(1 + x)^n = \displaystyle \sum^{n}_{r = 0} {^nC_r} x^r$$ then $$C^2_0 + \dfrac{C^2_1}{2} + \dfrac{C^2_2}{3} + ... + \dfrac{C^2_n}{n + 1} =$$

When $$n!+1$$ is divided by any natural number between $$2$$ and $$n$$ then remainder obtained is

The value of  $$\sum _ { r = 1 } ^ { 5 } r \dfrac { ^ { n } C _ { r } } { ^ { n } C _ { r - 1 } } =?$$