Question

1. in how many ways can a football team of 11 players be selected from 16 players ? how many of these will exclude 2 particular players ?
2. A contractor advertises for the post of carpenter he gets 7 equally qualified applicants and want to select 3 from them. in how many ways he can do it ?

Answer 1

$$\begin{gathered} 1.\left(\mathrm{a}\right) \\ \mathrm{Total}\mathrm{no}\mathrm{of}\mathrm{players}=16 \\ \mathrm{No}\mathrm{of}\mathrm{players}\mathrm{to}\mathrm{be}\mathrm{selected}=11 \\ \therefore \mathrm{No}\mathrm{of}\mathrm{ways}={}^{16}\mathrm{C}_{11}=\frac{16!}{11!.5!}=4368 \\ \left(\mathrm{b}\right): \\ \mathrm{No}\mathrm{of}\mathrm{ways}\mathrm{to}\mathrm{exclude}2\mathrm{particular}\mathrm{players}={}^{14}\mathrm{C}_{11}=\frac{14!}{11!.3!}=364 \\ 2. \\ \mathrm{Total}\mathrm{no}\mathrm{of}\mathrm{players}=7 \\ \mathrm{No}\mathrm{of}\mathrm{players}\mathrm{to}\mathrm{be}\mathrm{selected}=3 \\ \therefore \mathrm{No}\mathrm{of}\mathrm{ways}={}^7\mathrm{C}_3=\frac{7!}{3!.4!}=35 \end{gathered}$$