2.3 Permutations (in class)

3-digit numbers are constructed from the numbers 1, 2, 3, 4, 5, 6, and 7 using each number at most once. How many such numbers:

(a) can be constructed

(b) are even

(c) are odd

(d) are divisible by 3

(Calculator) The figure shows a street map in a city. Claire walks from [math]A[/math] to [math]B[/math]. She always walks to the right or upwards.

(a) How many possible routes does she have?

(b) How many possible routes does she have if she must pass through [math]C[/math] and [math]D[/math]?

The grid shown represent the street of downtown Taipei. Determine how many routes from A (Henri’s house) to B (Baltazer’s house) are possible if Henri only travels south or east.

There are 10 students with different heights in a line. Suppose for every student, the heights of the students next to them cannot both be higher than their own. How many permutations are there?

5-digit numbers are constructed from the digits 1, 2, 3, 4, and 5 using each digit once. Suppose we arrange these numbers from small to large:

(a) What is the [math]49^{\text{th}}[/math] number?

(b) Which number is 41325?

Use two colors of paint a die and each side has only one color, how many different combinations are there?

(Calculator) Jasmine, Jessica, Joseph, Jonathan, Charles, Courtney, Derek and Daniel are lining up to purchase tickets to the middle school musical Oliver. How many different arrangements are possible when they line up if:

(a) Jasmine has to be next to Jessica, but not next to Courtney

(b) Charles does not want to be next to a girl (Jasmine and Jessica are girls, the others are boys)