Permutation and Combination

A team of 10 players is to be chosen from 15 players. Find the number of different teams that can be chosen if there are no restrictions.

• 3003

• 303

• 33

• 3

A team of 10 players is to be chosen from 15 players. The 15 players include 3 sisters who must not be separated. Find the number of different teams that can be chosen.

• 792

• 66

• 858

• 27

A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The 6-digit number cannot start with 0 and all six digits must be different. Find how many 6-digit numbers can be formed if the 6-digit number is even.

• 42000

• 26880

• 15 120

• 53760

• 68 880

A 5-digit number is to be formed using 5 different numbers selected from 1, 2, 3, 4, 5, 6, 7, 8 and 9. No digit may be used more than once in any 5-digit number. Find how many 5-digit numbers can be formed.

• 15 120

• 15 000

• 11 000

• 12 000

A 5-digit number is to be formed using 5 different numbers selected from 1, 2, 3, 4, 5, 6, 7, 8 and 9. No digit may be used more than once in any 5-digit number. Find how many of these 5-digit numbers are greater than 50000 and even

• 3780

• 2520

• 1260

• 2100

A team of 9 people is to be chosen from 6 doctors, 4 dentists and 2 nurses. Find how many possible teams include at least 2 doctors, at least 2 dentists and at least 2 nurses.

• 116

• 36

• 60

• 20

A group of students, 4 girls and 3 boys, stand in line. Find the number of different ways the students can stand in line if there are no restrictions

• 5040

• 720

• 120

• 24

A group of students, 4 girls and 3 boys, stand in line. Find the number of different ways the students can stand in line if the 3 boys are next to each other.

• 720

• 120

• 6

• 1000

A group of students, 4 girls and 3 boys, stand in line. Cam and Dea are 2 of the girls. Find the number of ways the students can stand in line if Cam and Dea are not next to each other.

• 3600

• 5040

• 1440

• 1000

The number of combinations of n items taken 3 at a time is 92n. Find the value of the constant n.

• 25

• 20

• 15

• 28