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…

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
  1. \({ }^9 \mathrm{C}_4 \times{ }^8 \mathrm{C}_3 \times 3\) ! \(\times 4\) !
  2. \({ }^9 \mathrm{C}_4 \times{ }^8 \mathrm{C}_4 \times 4\) ! \(\times 4\) !
  3. \({ }^8 \mathrm{C}_3 \times{ }^8 \mathrm{C}_3 \times 4 ! \times 3\) !
  4. \({ }^9 \mathrm{C}_4 \times{ }^9 \mathrm{C}_4 \times 4\) ! \(\times 4\) !

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.

Asked in: AP EAMCET 2020 (18 Sep Shift 2)

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