A drawer contains 12 brown socks and 12 black socks, all unmatched.A man takes socks out at random in the dark.

Select the least number of socks that he must take out to be sure that he has at least two socks of the same color?

A multiple choice test contains 9 questions. There are four possible answers for each question.

In how many ways can a student answer the questions on the test if the student can leave answers blank?

There are 20 mathematics majors and 325 computer science majors in a college.

In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?

Find the number of strings of six lowercase letters from the English alphabet that contain the letters a and b?

One hundred tickets numbered 1,2,3,........100 are sold to 100 different people for a drawing. Four different prizes are awarded including a grand prize ( a trip to Tahiti). how many ways are there to award the prizes if it satisfies the given condition:

The person holding the ticket 47 does not win a prize.

How many strings of three decimal digits have exactly two digits that are 4s?

How many bit strings are there of length 6 or less not counting the empty string?

How many strings of four decimal digits end with an even digit?

7 women and 8 men are on the faculty in the mathematics department at a school.

How many ways are there to select a committee of five members if at least one woman and at least one man must be on the committee?

A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them.

How many balls must she select to be sure of having at least three balls of the same color?