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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
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..
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..
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..
Corollary 1:
C(n,r) = C(n,n-..
Row Matrix
A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..
Question 5
Question: Given five different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking atleast one green and one blue dye? Answer: The least number of dyes that a combination can have is 2. (one ..
Question 2
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1 = Sel..
Proof:
The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any ..
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