PERMUTATIONS AND COMBINATIONS

There are 720 different 5-digit numbers that can be formed using the digits 1, 2, 3, 5, 7, and 8, if each digit may be used only once in any number. How many of these 5-digit numbers are even and greater than 30000?

• 360
• 168

• 240
• 300

There are 720 different 5-digit numbers that can be formed using the digits 1, 2, 3, 5, 7, and 8, if each digit may be used only once in any number. How many of the 5-digit numbers are not divisible by 5?

• 720
• 576
• 648
• 600

The number of combinations of n items taken 3 at a time is 6 times the number of combinations of n items taken 2 at a time. Find the value of the constant n.

• n = 20

• n = 18

• n = 9
• n = 7

Find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit may be used only once in any number.

• 720
• 120
• 360
• 600

In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. Find the number of ways in which this can be done.

• 700 ways

• 420 ways
• 320 ways
• 280 ways

The digits of the number 6378129 are to be arranged so that the resulting 7-digit number is even. Find the number of ways in which this can be done.

• 2160

• 90720
• 362880
• 1814400

Jess wants to arrange 9 different books on a shelf. There are 4 mathematics books, 3 physics books and 2 chemistry books. Find the number of different possible arrangements of the books if all the mathematics books are kept together and all the physics books are kept together.

• 9!
• 4!*3!*2!*3!
• 4!*3!*4!

• 4!*3!*2!*2!

A team of 8 players is to be chosen from 6 girls and 8 boys. Find the number of different ways the team may be chosen if at least 1 girl is on the team.

• 5005
• 1287
• 3002

• 4004

Jack has won 7 trophies for sport and wants to arrange them on a shelf. He has 2 trophies for cricket, 4 trophies for football and 1 trophy for swimming. Find the number of different arrangements if the football trophies are to be kept together.

• 5040
• 576

• 144
• 2880

A quiz team of 6 children is to be chosen from a class of 8 boys and 10 girls. Find the number of ways of choosing the team if there are more boys than girls in the team.

• 3738

• 3150

• 3710

• 10458