Example 1:
There are 8 cars plying between two towns A and B. In how many ways can a person go from one town to the other and return by a different ca..
Question 1
\ n = ..
\ n = ..Question 1
or n < 2n Multiplying the above terms of both sides respectively, we get Multiplying both sides by n!, we get From (1) and (2), we g..
or n < 2n Multiplying the above terms of both sides respectively, we get Multiplying both sides by n!, we get From (1) and (2), we g..Corollary 1:
If we put r = n in the above formula, the..
If we put r = n in the above formula, the..Question 1
Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thin..
Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thin..Question 1
Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done in ..
Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done in ..Example 1:
1. Three boys and three girls are to be seated around a table in a circle. Among them, the boy X does not want any girl as neighbour and girl Y does not want any boy as neighbour. How many such arrangements are possibl..
Note 1:
Only a square matrix can have its invers..
Example 1:
Using matrix method solve the following systems of linear equations 2x - y + z = -3 3x - z = - 8 2x + 6y ..
Corollary 1:
C(n,r) = C(n,n-..
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