3. There are 21 different applications installed on the phone. In how many ways can six applications be selected for deletion so that among them are three applications from the following six $T V F T' V' F'$, but none of the pairs $T T', V V', F F'$ are included?
Answer. $8 \cdot C_{15}^{3}=3640$.

Solution. Choose one application from each pair $T T^{\prime}, V V^{\prime}, F F^{\prime}-8$ ways. Thus, out of 21 applications, 6 have already been excluded, leaving 15. Choose 3 applications from the remaining 15, which can be done in $\frac{15 \cdot 14 \cdot 13}{3!}$ (or $C_{15}^{3}$) ways. In total, $8 \cdot C_{15}^{3}=3640$.

Criteria. Full solution - 7 points. The idea to choose one application from each pair without further progress - 16.