Q81 / 160 · TS EAMCET 2017 · Mathematics

A village has 10 players. A team of 6 players is to be formed. 5 members are chosen out of these 10 players and then the captain is chosen from the remaining players. Then total number of ways of choosing such teams is

  • Correct answer
    A
    1260
  • B
    210
  • C
    $\left.{ }^{10} \mathrm{C}_6\right) 5$ !
  • D
    $\left({ }^{10} \mathrm{C}_5\right) 6$

Solution

Total number of ways of choosing such terms is $$ \begin{aligned} & { }^{10} C_5 \cdot{ }^5 C_1 \\ & =\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} \times 5 \\ & =10 \times 3 \times 7 \times 6=1260 \\ & \end{aligned} $$

Hence, the correct answer is option: 'A'.

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