Dear Reader, below are three probability related practice questions for Wipro and other similar papers. First one is simple while the remaining two are moderately difficult but employ similar logic.

Question 1

In a radio Station, the songs database contains songs from 2 Tamil movies, 1 Hindi movie and 1 Telugu movie. Each movie has 5 songs.They can play only 3 songs.If they want to play 3 tamil songs then what will be the probability?

a) 10C3 / 20C3 b) 5C3 / 15C3 c) 5C3 / 20C3 d) 20C3 / 10C3

Answer : a) 10C3 / 20C3

Solution :

Since each movie has 5 songs, the total number of songs is 20.
Out of 20 songs, they have to play 3 songs.
Therefore, number of ways of selecting 3 songs = 20C3.
Number of ways of selecting 3 Tamil songs = 10C3.
Probability of playing three tamil songs = Number of ways of selecting 3 Tamil songs / Number of ways of selecting 3 songs (any language) = 10C3 / 20C3.

Question 2

There are two cricket teams namely Team A and Team B. Each has 15 players (including substitutes). Now a new team of playing 11 has to be formed by pulling players from both the teams. In how many ways 11 players can be selected such that at least 5 players are picked from each team?

a) 15C5 x 15C6 b) 2(15C5 x 15C6) c) (15C5)² d) 15C6

Answer : b) 2(15C5 x 15C6)

Solution :

Since at least 5 players from each team should be pulled up the possible ways of selection are
5 players from Team A and 6 players from Team B (OR)
6 players from team A and 5 players from Team B.

Case I : Therefore, the number of way of selecting 5 players from Team A AND 6 players from Team B = 15C5 x 15C6.
Case II : Similarly, the number of way of selecting 6 players from Team A AND 5 players from Team B = 15C6 x 15C5.

Hence, the number of ways of selecting 11 players such that at least 5 players in each team = Case I OR Case II = 15C5 x 15C6 + 15C6 x 15C5
= 2(15C5 x 15C6)
P.S : In probability equations like those employed in the above question, AND's need to be replaced by 'x' (multiply) and OR needs to be replaced by '+' (addition).

Question 3

In a College, there are 10 students in Maths department, 12 Students in Computer Science department and 8 students in Physics department. A recruiting company wants to select 4 students out of these 30 students with at least 1 student from each department. In how many ways the company can achieve this ?

a) 12960 b) 12690 c) 19260 d) 16920

Answer :

Solution:

Since there should be at least 1 student from each department, the possible ways of selection are
1 Student from Maths, 1 student from computer science and 2 students from physics (OR)
1 Student from Maths, 2 students from computer science and 1 student from physics (OR)
2 Students from Maths, 1 student from computer science and 1 student from physics.

Note : Applying a very similar logic as that of the previous question,
Therefore, the number of ways of selecting 4 students such that at least 1 student from each department = 10C1 x 12C1 x 8C2 + 10C1 x 12C2 x 8C1 + 10C2 x 12C1 x 8C1
= (10 x 12 x 8 x 7)/2 + (10 x 12 x 11 x 8)/2 + (10 x 9 x 12 x 8)/2
= (10 x 12 x 8)(7+11+9)/2
= 10 x 12 x 8 (27/2)
= 480 x 27
= 12960