Combination Formula

A selection that can be formed by taking some or all finite set of things (or objects) is called a combination. Formation of a combination by taking ‘f’ elements from a finite set A containing ‘n’ elements means picking up f-elements subset of A ($n \geqslant f$).

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