Question

there are 3 mangoes 5 oranges and 6 apples in a fruit basket.what is the number of ways in which 10 fruits can be selected from the fruit basket?

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{ways}10\mathrm{fruits}\mathrm{can}\mathrm{be}\mathrm{selected}\mathrm{out}\mathrm{of}\left(3+5+6\right)=14\mathrm{fruits}={}^{14}\mathrm{C}_{10} \\ =\frac{14!}{4!\times 10!} \\ =\frac{14\times 13\times 12\times 11\times 10!}{4\times 3\times 2\times 1\times 10!} \\ =1001 \end{gathered}$$