7.

5.

1
probability that none of them are white.

a. How many ways are there to choose 6 items from 10 distinct items when

(i) the items in the choices are ordered and repetition is not allowed?

(ii) the items in the choices are ordered and repetition is allowed? (4) (iii)
the items in the choices are unordered and repetition is not allowed? (iv) the
items in the choices are unordered and repetition is allowed?
Admission to a foreign university is determined by an entrance examination, with its
scores normally distributed with a mean of 500 and a standard deviation of 100. A

student will be admitted to the university if he scores better than at least 70% of the
students who wrote the entrance. (5)

(i) Alice scored 585 marks. Will he be admitted to the university?

(ii) Bob says he will not get admission in the university. What will be his marks?
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a. Show that in a group of 10 people (where any two people are either friends or

enemies), there are either three mutual friends or four mutual enemies and (5) there
are either three mutual enemies or four mutual friends.

b. (i) Explain continuous and discrete random variables. (4)

(ii) Write the properties of a standard normal curve.

PART C
a. Define the following with an example:
(1) n-dimensional hypercube (6)
(ii) planar graph
(iii) decision tree
(iv) bipartite graph

b.If © is a group whose table is given below. Show that H={1,c,d} and രവം
both subgroups of G. Find the left coset aH and the right coset Ka.