If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

If $P(56, r+6) : P(54, r+3) = 30800 : 1$,find $r$.

How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to