[Maths Class Notes] on Combination Formula Pdf for Exam

The number of combinations of n dissimilar things taken ‘k’ at a time or choosing k objects or things from n objects is denoted by 

[^{n}c_{k}:  or: C(n,K) : or: C binom{n}{k} or: binom{n}{k}]

 

[^{n}c_{k} = frac{n!}{k!(n-k)!}]

Example: 

If there are 12 persons in a party, and if each two of them shake hands with each other, the number of handshakes in the part is _____

Solution: It is to note that, when two persons shake hands, it is counted as one handshake. The total numbers of handshakes is some as the number of ways of selecting 2 persons among 12 persons.

Thus,

[^{12}c_{2}  = frac{12!}{10!2!}]  = 66

Question:

No. of ways of selecting 2 girls and 3 boys from 3 girls and 5 boys is 

Options:

(a) 20

(b) 24

(c) 30

(d) 48