Q110 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

The crew of an 8-oar boat is to be chosen from 12 men, of whom 3 can row on the stroke side only. The number of ways in which the crew can be arranged is

  • A
    \({ }^9 \mathrm{C}_4 \times{ }^8 \mathrm{C}_3 \times 3\) ! \(\times 4\) !
  • Correct answer
    B
    \({ }^9 \mathrm{C}_4 \times{ }^8 \mathrm{C}_4 \times 4\) ! \(\times 4\) !
  • C
    \({ }^8 \mathrm{C}_3 \times{ }^8 \mathrm{C}_3 \times 4 ! \times 3\) !
  • D
    \({ }^9 \mathrm{C}_4 \times{ }^9 \mathrm{C}_4 \times 4\) ! \(\times 4\) !

Solution

Crew side \(=4 \rightarrow 4\) ! ways Stroke side \(=4 \rightarrow 4\) ! ways Total number of ways \(={ }^9 C_4 \times{ }^8 C_4 \times 4 ! \times 4 !\) Hence, option (b) is correct.

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

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