The number of words with or without meaning can be formed from the word $\mathrm{MATHEMATICS}$ when $C, S$ does not come together is

How many numbers of four digits can be made by using the digits $3, 5, 6, 7,$ and $9$?  (Repetition of digits is not allowed)

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

Let $S_1=\left\{\left(i,j,k\right) :i,j,k\in \left\{1,2,\dots ,10\right\}\right\}$

$S_2=\left\{\left(i,j\right) :1\le i<j+2\le 10,i,j\in \left\{1,2,\dots ,10\right\}\right\}$

$S_3=\left\{\left(i,j,k,l\right):1\le i<j<k<l,i,j,k,l\in \left\{1,2,\mathrm{.....},10\right\}\right\}$

and  $S_4=\left\{\left(i,j,k,l\right) : i,j,k \text{and} l \text{are distint elements in} \left\{1,2,...,10\right\}\right\}$

If the total number of elements in the set $S_r$ is $n_r,r=1,2,3,4$ then which of the following statements is (are) TRUE?