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 $^n{C_k}\,\,{\text{or }}C\left( {n,k} \right)\,\,{\text{or }}C\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right)\,\,\,{\text{or }}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right).$ Also $^n{C_k} = \frac{{n!}}{{k!\left( {n - k} \right)!}}$
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