PERMUTATIONS AND COMBINATIONS

How many 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7, and 8, that are even and greater than 30000?

How many 5-digit numbers formed using the digits 1, 2, 3, 5, 7, and 8 (each used once) are not divisible by 5?

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.

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.

Select 2 questions from 5 in section A and 4 questions from 8 in section B. How many ways can this be done?

Arrange the digits of 6378129 to form an even 7-digit number. How many ways can this be done?

Arrange 9 books: 4 math, 3 physics, 2 chemistry. Math and physics books must be kept together.

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.

Jack has 7 trophies: 2 cricket, 4 football, 1 swimming. How many arrangements if football trophies are together?

Number of ways to choose a team of 6 children from 8 boys and 10 girls, with more boys than girls.