Question

In how many ways can a football team of $11$ players be selected from $16$ players? How many of them will (i) include $2$ particular players? (ii) exclude $2$ particular players?

• A. $^{16}C_{9}, \,^{14}C_{11}$
• B. $^{14}C_{9}, \,^{14}C_{11}$
• C. $^{14}C_{9}, \,^{16}C_{11}$
• D. None of these

Answer 1

Answer: (B)

$^{14}C_{9}, \,^{14}C_{11}$

Answer 2

Total number of players = $16$ $\therefore$ No. of ways of selecting $11$ players out of $16$ players $= \,^{16}C_{11}$ . (i) If $2$ particular players are included then number of ways $= \,^{16-2}C_{2} = \,^{14}C_{9}$ (ii) If $2$ particular players are excluded then number of ways $= \,^{16-2}C_{11} = \,^{14}C_{11}$