Today’s topic is Combinations (Selection, committee, group)
Each of the different groups or selections which can be formed by taking some or all of a number of objects called combinations.
Suppose we want to select two out of three persons A, B, C. Then possible selections are AB, BC, CA
Note – AB and BA represent the same selection.
Suppose we want to select three out of three persons A, B, C. Then possible selections are ABC.
Note – ABC and BAC and CAB are the same selection.
Number of Combinations –
If (n=r), then nCn = 1 and nCo = 1
nCr = nC(n-r)
16C13 = 16C16-13 = 16C3
Let’s discuss some examples –
Find the value of 5C2
Find the value of n when nC2 = 105?
nC2 = 105
There are 15 persons in a group. They hand shake to each other. Find the different number of handshake.
Example – 4
From a group of 10 men and 5 women. 4 persons are to be selected to form a committee. Find the different number of ways of selection.
From the group of 10 men and 5 men. 4 persons to be selected such that 3 men and 1 woman to be selected to form a committee. Find the different number of ways of selection.
From a group of 10 men and 5 women. 4 persons are to be selected such that 4 men or 4 women in the group. Find the different number of ways.
A committee of 5 members is to be formed out of 4 men and 5 women.
(i) In how many ways can a committee consisting of at least 1 woman be formed?
5C1 × 4C4 + 5C2 × 4C3 + 5C3 × 4C2 + 5C4 × 4C1 + 5C5 × 4C0
= 5 × 1 + 10 × 4 + 10 × 6 + 5 × 4 + 1
(ii) In how many ways can a committee consisting of 3 men and 2 women be formed?
With this, we will finish this topic.
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