Permutations an...

$$\sum _{ k=1 }^{ 10 }{ k.k! } =$$

Solve:
$$\dfrac{^{n}C_{r}}{^{n}C_{r-1}}=$$

The number of was dividing $$52$$ cards amongst four players equally, are 

A double Decker is can accommodate 20 passengers 7 in the lower deck 13 in the upper deck. The number of ways the passengers can be accommodate if 5 want to sit only in lower deck and 8 want to sit only in upper deck is 

The number of words which can be made out of the letters of the word $$'MOBILE'$$ when consonants always occupy odd places is _______.

If $$^{n}C_{4},\ ^{n}C_{5}$$ and $$^{n}C_{6}$$ in A.P., then possible value of $$n$$ is

How many 10 digits number can be written by using digits (9 and 2) ?

If $$CARPET$$ is coded as $$TCEAPR$$ then the code for $$NATIONAL$$ would be written as 

All possible three digits even numbers which can be formed with the condition that if $$5$$ is one of the digit, then $$7$$ is the next digit is:

A committee of $$10$$ is to be formed from $$8$$ women and $$6$$ men. In how many of these committees the women are in majority?