Math for Computer science
Questions 151 to 160
151.

Let A = {a, b}
and B be the set of all strings over A. The function g: B →Z is defined
as g(S) = the number of a’s
in S, for each string S ∈B. Then g (ababb) =


How many
different permutations can be formed out of all the letters of the word
“MATHS”?


How many
different permutations can be formed out of the letters of the word
“MISSISSIPPI”?


How many groups
of 4 people can be formed from 6 people?


How many ways
can 5 persons arrange themselves around a circular table?


Ten balls
numbered 0, 1, 2, ….., 9 are put in a box and two balls are taken at random
without replacement. The probability
that both numbers are odd is equal to


A box contains 4
red balls and 2 white balls. Another box contains 5 red balls and 3 white
balls. Abox is selected at random and then a ball is drawn at random. The
probability that the ball is white is equal to


If A and B be
two events with P(A) = , P(B) = and P(A È B) = , then P(A/B) =


If A and B be
two events with P(A) = , P(B) = and P(A Ç B) = , then P(Ac Ç Bc) =


It is given that
p → q, q → r and r → s are true. Which of the following must be necessarily
true?

Answers
151.

Answer : (b)
Reason : by
the definition of function the number of a’s are in the given string is 2

Answer : (d)
Reason : by
the definition of permutations the number of ways are (5!)


Answer : (c)
Reason : by
the definition of permutations with indistinguishable objects the number of ways are (11!) / (2! 4! 4!)


Answer : (a)
Reason : 4
people has to be selected from 6 people which can be done in C(6,4) ways = 15
ways


Answer : (b)
Reason : by
circular permutation the number of
ways are (51)! = 4! = 2456


Answer : (d)
Reason : The
no. of ways choosing 2 balls is C (52,2 ).
The first odd number can be drawn in C(5,2 ) ways and that of second
odd number in C(4,2 ) ways . the probability is given by 4/9 ( after simplification of [C(5,2 )x C(4,2 )] / C (52,2 ) )


Answer : (d)
Reason : The
probability of choosing a box is ½.
The white ball choosing from 1 box is 2/6 and
The white ball choosing from 2 box is 3/6 so the required probability
is 1/6+3/16


Answer : (c)
Reason : P(AÇB)
= 0 so
P(A/B) = 0


Answer : (b)
Reason : By
the Addition theorem on
probability , P(Ac Ç
Bc) = 1 P (AÈ B )
= 1 – (7/9)
=2/9


Answer : (d)
Reason : By
the definition of Hypothetical
syllogism

incomplete answer choice
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