Suppose $A$ is denoted the set of all numbers between 1 and 700 which are divisible by 3 and let $B$ is denoted the set of all numbers between 1 and 300 which are divisible by 7 . If $C=\{(a, b) \mid a \in A, b \in B, a \neq b$ and $a+b=$ even number $\}$, then order of C is

If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is

The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is

The numbers $$1,2,3, \ldots \ldots, \mathrm{m}$$ are arranged in random order. The number of ways this can be done, so that the numbers $$1,2, \ldots \ldots ., \mathrm{r}(\mathrm{r}<\mathrm{m})$$ appears as neighbours is