Probability Questions

A clerk is given 3 letters written in a language unknown to her. She is also given an envelope with an address corresponding to each letter written in the same language. If the clerk puts the letters in the envelopes, in how many ways can she do it so that none of the 3 envelopes contains the letter with the correct address?

How many ways a captain and a vice-captain can be selected from a team of 11 players?

A committee of $3$ members is to be formed from $5$ men and $4women$. What is the probability that the committee contains at least one woman?

What is the probability of drawing an ace from a pack of 52 cards?

From a group of $7\text{men}$ and $6\text{women}$, five persons are to be selected to form a committee so that at least $3\text{men}$ are there in the committee. In how many ways can it be done?

A box contains $15$ marbles out of which $4$ are white, $5$ are red and $6$ are blue. Three balls are to be drawn at random from the bag. What is the probability that all of them are red?

A problem is given to three students whose chances of solving it are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved?

A bag contains $4$ White shirts, $4$ Black shirts and $6$ Pink shirts. If two shirts are drawn randomly, what is the probability that at most one shirt is white?