Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?

The probability of $A, B, C$ solving a problem are $\frac{1}{3}, \frac{2}{7}, \frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously,the probability that exactly one of them will solve it,is

Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

Three dice are thrown. The sum of the numbers is $15$. What is the chance of getting $4$ on the first die?

$A$ single letter is selected at random from the word $PROBABILITY$. The probability that the selected letter is a vowel is

$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.