Permutations warm-up 2

6

How many arrangements of letters the set {a, b, c, d, e} are there if the arrangements must start with an 'a' and end with an 'e'? (assume each letter is only used once)

24

How many arrangements of the letters the set {a, b, c, d, e} contain the sequence 'de' somewhere? (Assume each letter is used exactly once)

13

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 blue balls?

720

How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9 inclusive?

* P(10,10) + P(11,6) = P(10!) * P(11,6) = 10! * 11!/6!(5!) = 3,628,800 * 332,640 = 1,207,084,032,000

How many ways are there for 10 women and six men to stand in a line so that no two men stand next to each other? [Hint: First position the women and then consider possible positions for the men.]

30240

How many ways are there to form a line of 5 people from a group of 10 people?

120

In how many ways can we arrange five students in a line for a picture?

210

In how many ways can we arrange three students from a group of seven students to stand in line for a picture?

3628800

Suppose that a saleswoman has to visit eleven different cities. She must begin her trip in a specified city, but she can visit the other ten cities in any order she wishes. How many possible orders can the saleswoman use when visiting these cities?