BCA Semester 1 – Mathematics I – Unit 6: Permutation and Combination

a) If $A, G,$ and $H$ are the arithmetic, geometric, and harmonic means between two unequal positive numbers, prove $A>G>H$.
b) State the relation between permutation and combination of n objects taken r at a time. A committee of 5 is formed from 6 boys and 5 girls. How many ways include at least one boy and one girl?

How many numbers of at least three different digits can be formed using the digits $1, 2, 3, 4, 5, 6?$

A committee of $5$ is to be constituted from $6$ boys and $5$ girls.
How many ways can this be done to include at least one boy and one girl?

a) A bag contains $8$ red balls and $5$ blue balls.
In how many ways can $3$ red balls and $4$ blue balls be drawn?

b) Find the volume of the parallelepiped whose concurrent edges are represented by the vectors:

There are 7 men and 3 ladies. Find the number of ways in which a committee of 6 persons can be formed if the committee should have at least one lady.

How many numbers of three different digits less than $500$ can be formed from the integers $1, 2, 3, 4, 5, 6$?