A combination is a selection of objects without regard to order.
Problem 1 :
How many different teams of 4 can be selected from a squad of 7 if,
i) there are no restrictions
ii) the teams must include the captain ?
Solution :
Total number of players = 7
number of players to be selected = 4
i) since there is no restriction, the number of ways be^{ 7}C_{4}
= 7!/(7-4)! 4!
ii) There must be 1 player to be selected for captain. From the remaining 6 player, 4 players should be selected.
Problem 2 :
If there are 12 persons in a party and if each two of them shake hands with each other, how many handshakes happen in the party ?
Solution :
Problem 3 :
A question paper has two parts, Part A and Part B each containing 10 questions. If a student to choose 8 from Part A and 5 from Part B, in how many ways can he choose the questions ?
Solution :
So, the required number of ways are 11340.
Problem 4 :
In how many ways a committee of 5 members can be selected from 6 men and 5 women consisting of 3 men and 2 women ?
Solution :
Problem 5 :
In how many ways can a cricket eleven be chosen out of a batch of 15 players if
i) there is no restriction on the selection
ii) a particular players is always chosen ?
iii) a particular player is never chosen ?
Solution :
i) Total number of players = 15
number of players to be selected = 11
ii) one person always to be chosen means, 10 persons are selected from the total of 14 players.
iii) By leaving one particular person, we have total of 14 choices.
Problem 6 :
How many chords can be drawn through 21 points on a circle?
Solution :
By joining any two points on the circle, we can create a chord. Even diameter is also chord, but chord is not a diameter.
Problem 7 :
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide either all of them will join or none of them will join. In how many ways can they be chosen ?
Solution :
i) All 3 students should join :
Let us consider the three students has been joined and the remaining 7 students alone can be selected from 22.
ii) Those three students doesn't join :
Number of ways that any one of it happen :
(1) + (2)
= 170544 + 646646
= 817190
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM