Sequences and S...

The number of seven letter words that can be formed by using the letters of the word  $$SUCCESS$$  that the two  $$C$$ are together but no two  $$S$$  are together is

Find the missing number :

Find the missing number.

The value of $$^{47}C_{4}+\displaystyle \sum _{ j=1 }^{ 5 }\ ^{ \left( 52-j \right)  } { C }_{ 3 }$$ is

$$496 : 204 : : 329 : ?$$

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 :

Find the sum of first $$15$$ terms of the sequence whose $${n}^{th}$$ term is $$3+4n$$.

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

solve

insert the missing number:  5,8,12,17,23,___,38