Q3:W3:Pretest

Six math books, five science books, and two English books are to be arranged on a shelf, so that books of the same subject must be together. How many ways can this be done?

• 6! ⋅ 5! ⋅ 2!

• 6! ⋅ 5! ⋅ 2! ⋅ 3!

• 6 ⋅ 5 ⋅ 2

• 6 ⋅ 5 ⋅ 2 ⋅ 3

How many ways can you arrange the letters of the word EDUCATION, such that the vowels are always together?

• 120

• 14400

• 362880

• 6547234

In a basketball tournament, there are a total of 45 games played. If each team plays with other teams once, how many teams joined the tournament?

• 5

• 10

• 15

• 20

How many polygons can be possibly formed from 6 distinct points on a plane, no three of which are collinear?

• 10

• 38

• 42

• 56

In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 followed by 3 letters from the alphabet. How many number plates can be formed if neither the digits nor the letters are repeated?

• 47,174,400

• 327,600

• 18,624

• 2,726