91Ó°ÊÓ

For the sum $$\sum_{i=1}^{n} a_{i}, $$ \(i\) is called the _____ of summation, \(n\) is the _____ limit of summation, and 1 is the _____ limit of summation.

Using Pascal's Triangle In Exercises 15-18, evaluate using Pascal's Triangle. $$\left( \begin{array}{l}{6} \\ {5}\end{array}\right)$$

True-False Exam In how many ways can you answer a 12 -question true-false exam? (Assume that you do not omit any questions.)

License Plate Numbers In the state of Pennsylvania, each standard automobile license plate number consists of three letters followed by a four-digit number. How many distinct license plate numbers can be formed in Pennsylvania?

License Plate Numbers \(\operatorname{In}\) a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and "zero" and between "I" and "one," the letters "O" and "I" are not used. How many distinct license plate numbers can be formed in this state?

Proving an Inequality In Exercises \(25-30\) , use mathematical induction to prove the inequality for the indicated integer values of \(n .\) $$n !>2^{n}, \quad n \geq 4$$

Concert Seats Four couples have reserved seats in one row for a concert. In how many different ways can they sit when (a) there are no seating restrictions? (b) the two members of each couple wish to sit together?

Single File In how many orders can four girls and four boys walk through a doorway single file when (a) there are no restrictions? (b) the girls walk through before the boys?

Posing for a Photograph In how many ways can five children posing for a photograph line up in a row?

Riding in a Car In how many ways can six people sit in a six-passenger car?