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Discrete math is the branch of mathematics which deals with objects that can have distinct values. The term discrete is used in contrast with continuous. Discrete objects require integers whereas continuous objects require real numbers. The discrete mathematics is used in fields such as number theory, graph theory and theory of computation. The study of discrete mathematics includes study of algorithm and their implementations. The importance of discrete mathematics is increased more in recent times. Research in discrete mathematics is also increased more due to development of computers.

**Problem 1: A five digit number is in specific order and the digits are between 0 - 9. How many different numbers can be formed if one digit can be used only once?**

**Solution: **Given the five digit number is in specific order. Here the order matters so we may use permutation.

=> P (n, r) = n! / (n-r)!

=> n is number of number of digits 0 – 9 = 10

=> r = 5 digit number

=> P (10, 5) = 10! / (10 – 5)!

= (10* 9* 8* 7* 6* 5* 4* 3* 2* 1) / 5* 4* 3* 2* 1= 25200

**=> The number of 5 digit numbers formed = 25200**

**Problem 2: In how many ways 6 students from a group of 15 students can be lined up for a program? **

**Solution: **The number of students = 15

=> 6 students are lined up from group of 15 students

=> P (n, r) = n! / (n-r)!

=> n is number of number of digits 0 – 9 = 10

=> r = 5 digit number

=> P (10, 5) = 10! / (10 – 5)!

= (10* 9* 8* 7* 6* 5* 4* 3* 2* 1) / 5* 4* 3* 2* 1= 25200

=> 6 students are lined up from group of 15 students

=> There are P (15, 6) possible permutations of 6 students from a group of 15 students.

=> P (15, 6) = 15! / (15 – 6)! = 15! / 9! = 3603600

**=> There are 3603600 different lines can be formed.**

=> P (15, 6) = 15! / (15 – 6)! = 15! / 9! = 3603600