Pnc Probability Handout Worksheet - Cet King
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2PnC Probability Handout
WORDS
Answer the questions on the basis of the information given below. A string of three English letters is formed as per
the following rules:
I. The first letter is any vowel.
II. The second letter is m, n or p.
III. If the second letter is m, then the third letter is any vowel which is different from the first letter.
IV. If the second letter is n, then the third letter is e or u. V.
If the second letter is p, then the third letter is the same as the first letter. (2003)
1. How many strings of letters can possibly be formed using the above rules? 1. 40
2. 45
3. 30
4. 35
2. How many strings of letters can possibly be formed using the above rules such that the third letter of the
string is e?
1. 8
2. 9
3. 10
4. 11
PATHS
3. The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible
direction of travel. What is the number of distinct paths from A to F? (2001)
a)9 b)10
c)11
d)None
4. In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards.
Along how many distinct routes can a car reach point B from point A? (2004)
a)15
b)56
c)120
d)336
The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is
situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
5. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of
possible shortest paths that she can choose is (2008)
(1) 60 (2) 75 (3) 45 (4) 90 (5) 72
6. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number
of possible shortest paths that she can choose is (2008)
(1) 1170 (2) 630 (3) 792 (4) 1200 (5) 936
SELECTION
7. There are 10 points on a line and 11 points on another line, which are parallel to each other. How many
triangles can be drawn taking the vertices on any of the line? (1999)
(a) 1050 (b) 2550 (c) 150 (d) 1045
8. A man has nine friends – four boys and five girls. In how many ways can he invite them, if there have to be
exactly three girls in the invitees? (1996)
(a) 320 (b) 160 (c) 80
(d) 200
Circles
9. Seven men and seven women have to sit around a circular table so that no 2 women are together. In how
many different ways can this be done?
a)6!*7!
b)6!*6!
c)6!*5!
d)6!*4!
10. In how many ways can 8 directors, a vice chairman and a chairman of a firm be seated at a round table, If the
chairman has to sit between the vice chairman and the director?
(a)9! x 2 (b)6! x 2 (c)8! x 2
(d)7! x 2
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