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This is solution to assignment of Basic Mathematics course. This was submitted to Karunashankar Sidhu at Institute of Mathematical Sciences. It includes: Variance, Combinations, Committees, Graph, Hamilton, Circuit, Vertex, Degree
Typology: Exercises
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Maximum Marks: 15
Question 1 Mark: 5
There are 8 men and 10 women members of a club. How many committees of seven persons can be formed, having 4 women?
Solution: We have to form combinations of 4 women out of 10 and 3 men out of 8. 10 C 4 (^) =210 and 8 C 3 (^) =
Total number of ways are
10 8 C 4 (^) C 3 210 56 11760
Question 2 Marks: 5
Compute x and x for x = –3.
Solution:
Question 3 Marks: 5
(a) Determine whether the given graph has a Hamilton circuit? If it does, find
such a circuit, if it does not , given an argument to show why no such circuit
exists. (Marks=2)
(b) Give the degree of each vertex in the figure (given below) (Marks=3)
Solution(a): a, b, c, d, e, a is Hamilton circuit
Solution(b): Deg(A) = Deg(D) = 1 , Deg(B) = Deg(C) = 3