Page 83 - DMTH404_STATISTICS

Unit 6: Probability

Solution. Notes

The journey from Delhi to Port-Blair can be treated as three operations; From Delhi to Allahabad,
from Allahabad to Calcutta and from Calcutta to Port-Blair. Using the fundamental principle of
counting, the journey can be planned in 4 4 2 = 32 ways.

Example 10: In how many ways the first, second and third prize can be given to 10
competitors?
Solution.

There are 10 ways of giving first prize, nine ways of giving second prize and eight ways of
giving third prize. Therefore, total no. ways is 10  9 8 = 720.
Alternative method :

10!
10
Here n = 10 and r = 3,  P = = 720
3
(10 3- )!
Example 11:
(a) There are 5 doors in a room. In how many ways can three persons enter the room using
different doors?
(b) A lady is asked to rank 5 types of washing powders according to her preference. Calculate
the total number of possible rankings.

(c) In how many ways 6 passengers can be seated on 15 available seats.
(d) If there are six different trains available for journey between Delhi to Kanpur, calculate
the number of ways in which a person can complete his return journey by using a different
train in each direction.
(e) In how many ways President, Vice-President, Secretary and Treasurer of an association
can be nominated at random out of 130 members?
Solution.
(a) The first person can use any of the 5 doors and hence can enter the room in 5 ways.
Similarly, the second person can enter in 4 ways and third person can enter in 3 ways.
5!
Thus, the total number of ways is 5 P = = 60 .
3
2!
(b) Total number of rankings are 5 P = 5! = 120 . (Note that 0! = 1)
5
0!
(c) Total number of ways of seating 6 passengers on 15 seats are
15!
15
P = = 36,03,600.
6
9!
(d) Total number of ways of performing return journey, using different train in each direction
6
are 6 5 = 30, which is also equal to P .
2
(e) Total number of ways of nominating for the 4 post of association are
130!
130
P = = 27,26,13,120 .
4
126!

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