How many ways can a group of six boys and six girls be seated in a row of twelve seats if boys and girls must alternate in the row?

How many ways can 6 different contracts be distributed amongst 9 different firms, if any one firm can be awarded multiple contracts?

In a certain country, area codes have five digits and are subject to the following restrictions. The first digit cannot be 0,1,2,or3; the second digit can only be 0,1,2,3,or4; and there are no restrictions on the remaining digits. How many different area codes are possible?

How many three-digit numbers may be formed using elements from the set{1,2,3,4,5,6,7,8}

if no element may be used more than once in a number and the number must be even

A club with 134 members is to choose three officerspresident, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?