TS EAMCET · Maths · Permutation Combination
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
- A 1260
- B 210
- C \(\left.{ }^{10} \mathrm{C}_6\right) 5\) !
- D \(\left({ }^{10} \mathrm{C}_5\right) 6\)
Answer & Solution
Correct Answer
(A) 1260
Step-by-step Solution
Detailed explanation
Total number of ways of choosing such terms is \[ \begin{aligned} & { }^{10} C_5 \cdot{ }^5 C_1 \\ & =\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} \times 5 \\ & =10 \times 3 \times 7 \times 6=1260 \\ & \end{aligned} \]
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