Total players = 17, No. of bowlers = 5, No. of non-bowlers = 12 No. of ways of selecting 4 bowlers = $\,{}^{5}C_{4}$ No. of ways of selecting 7 non-bowlers = $\,{}^{12}C_{7}$ ∴ Required no. of ways of selecting a cricket team = $\,{}^{5}C_{4}$ × ${}^{12}C_{7}$ = $\frac{5!}{4! \times 1!} \times \frac{12!}{7! \times 5!}$ = 5 × $\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2}$ = 3960