Question

In how many ways can a captain and a vice-captain be selected from a team of 11 players

Answer 1

Answer:

captain and vice-captain are only one in a particular cricket team

so in order to select captain out of 11 players it can be done in 11C1 ways.

now since 1 person is selected remaining players are 10 out of which vice-captain is to be chosen so it can be done in 10C1 ways.

therefore total ways are=11C1*10C1=110 ways..............

Answer 2

Answer:

Step-by-step explanation:

The Total vice-captain to be selected from 11 players is 1

The Total Captain to be selected from 11 players is 1

11$c_{1}$×10$c_{1}$

From that 11 player the captain to be selected is

11$c_{1}$= $\frac{11!}{1!(11!-1!)}$

11$c_{1}$=$\frac{11!}{1!(10!)}$

11$c_{1}$=$\frac{11!}{10!}$

11$c_{1}$=(11×10×9×8×7×6×5×4×3×2×1)/(10×9×8×7×6×5×4×3×2×1)

11$c_{1}$=11--> For selecting Captain

So we selected captain from 11 players

Remaining players is 10

10$c_{1}$= $\frac{10!}{1!(10!-1!)}$

10$c_{1}$= $\frac{10!}{1!(9!)}$

10$c_{1}$= $\frac{10!}{9!}$

10$c_{1}$= (10×9×8×7×6×5×4×3×2×1)/(9×8×7×6×5×4×3×2×1)

10$c_{1}$=10

So multiply two possibilities

11$c_{1}$×10$c_{1}$=11×10=110